Yr Athro Tomasz Brzezinski

Athro

Mathematics

t.brzezinski@abertawe.ac.uk

305
Trydydd Llawr
Y Ffowndri Gyfrifiadol
Campws y Bae

Ar gael ar gyfer Goruchwyliaeth Ôl-raddedig

Dolenni Ymchwil

https://orcid.org/0000-0001-6270-3439

ResearchGate

ResearcherID

Trosolwg

Rwy'n fathemategydd sy'n arbenigo ar Algebra (yn enwedig astudiaethau o strwythurau algebraidd amrywiol fel modrwyau, modiwlau, cyd-fodrwyau, cydfodiwlau, algebrâu Hopf ac ati), Geometreg Anghymudol (algebraidd a differol, gyda phwyslais penodol yn cael ei roi ar agweddau cymesuredd), Theori Categori a rhai agweddau ar Ffiseg Fathemategol (grwpiau cwantwm, systemau integradwy). Rwy'n awdur neu'n gydawdur monograff a thros 110 o bapurau (a ysgrifennwyd gyda rhyw 45 o gyd-awduron). Efallai mai adfywiad a datblygiad sylweddol theori cyd-fodrwyau (categori dosbarthu AMS newydd wedi'i greu ar gyfer cyd-fodrwyau a chydfodiwlau o ganlyniad i'r gweithgaredd hwn) yw cyflawniad mwyaf nodedig fy rhaglen ymchwil.

Dechreuwyd ar y gwaith hwn wrth i M Takeuchi sylwi y gellir ystyried modiwlau sydd wedi'u plethu fel cyd-fodiwlau cyd-fodrwy. Datblygwyd y sylw hwn gyntaf yn [T. Brzeziński, The structure of corings. Induction functors, Maschke-type theorem, and Frobenius and Galois-type properties, Algebras and Representation Theory 5: 389-410, 2002] a denodd sylw'r gymuned fathemategol ehangach ar unwaith (yn ôl MathSciNet, y papur hwn yw'r erthygl y cyfeiriwyd ati fwyaf ond un o dros 1000 o bapurau a gyhoeddwyd yn y cyfnodolyn Algebras and Representation Theory). Arweiniodd astudiaethau cychwynnol o strwythur cyd-fodrwyau at fonograffeg a gafodd dderbyniad da iawn [T. Brzeziński ac R. Wisbauer, Corings and Comodules, Gwasg Prifysgol Caergrawnt, Caergrawnt 2003] a gwelwyd astudiaethau pellach yn fuan wedi hynny. Atyniad cyd-fodrwyau yw'r ffaith eu bod yn cyfuno gwahanol feysydd mathemateg: Theori algebra Hopf, geometreg anghymudol (differol ac algebraidd - sy'n ddamcaniaethau eithaf gwahanol i'w gilydd), theori modrwy a modiwl a theori categori (gan gynnwys, yn benodol, ei chymwysiadau i wyddoniaeth gyfrifiadurol). Gall y ffaith bod cyd-fodrwyau wedi'i gynnwys fel pwnc yn Nosbarthiad Pwnc Mathemateg Cymdeithas Fathemategol America o 2010 ymlaen fod yn arwydd o gydnabod cyd-fodrwyau gan y gymuned fathemategol ryngwladol.

Meysydd Arbenigedd

Algebra
Geometreg Anghymudol
Theori Categori
Algebrau Hopf
Cyd-fodrwyau a chyd-fodiwlau
Theori modrwyau
Theori modiwlau
Strwythurau algebraidd

Cyhoeddiadau

Uchafbwyntiau Ymchwil

Brzezinski, T. (2022). Lie trusses and heaps of Lie affebras. In Proceedings of Corfu Summer Institute 2021 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2021)Sissa Medialab.
https://doi.org/10.22323/1.406.0307, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa62196
Brzezinski, T. (2023). Homothetic Rota–Baxter Systems and Dyck$$^m$$-Algebras. Springer Proceedings in Mathematics & Statistics (pp. 103-110). Springer Nature Singapore
https://doi.org/10.1007/978-981-19-4751-3_7, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa62800
http://dx.doi.org/10.1007/978-981-19-4751-3_7
Andruszkiewicz, R., Brzezinski, T., & Rybołowicz, B. (2022). Ideal ring extensions and trusses. Journal of Algebra, 600, 237-278.
https://doi.org/10.1016/j.jalgebra.2022.01.038, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa60087
Brzezinski, T., Rybołowicz, B., & Saracco, P. (2022). On functors between categories of modules over trusses. Journal of Pure and Applied Algebra, 226(11), 107091
https://doi.org/10.1016/j.jpaa.2022.107091, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa59386
Brzezinski, T. & Rybołowicz, B. (2020). Modules Over Trusses vs Modules Over Rings: Direct Sums and Free Modules. Algebras and Representation Theory
https://doi.org/10.1007/s10468-020-10008-8, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa57814
Breaz, S. & Brzezinski, T. (2021). The Baer–Kaplansky Theorem for all abelian groups and modules. Bulletin of Mathematical Sciences, 12(01), 1-12.
https://doi.org/10.1142/s1664360721500053, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa56478
Brzezinski, T., Mereta, S., & Rybolowicz, B. (2022). From pre-trusses to skew braces. Publicacions Matemàtiques, 66(2), 683-714.
https://doi.org/10.5565/publmat6622206, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa56171
Brzezinski, T. & Szymański, W. (2021). An algebraic framework for noncommutative bundles with homogeneous fibres. Algebra & Number Theory, 15(1), 217-240.
https://doi.org/10.2140/ant.2021.15.217, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa54834
Brzezinski, T., Koenig, S., & Külshammer, J. (2020). From quasi‐hereditary algebras with exact Borel subalgebras to directed bocses. Bulletin of the London Mathematical Society, 52(2), 367-378.
https://doi.org/10.1112/blms.12331, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa53009
Brzezinski, T. & Rybolowicz, B. (2020). Congruence classes and extensions of rings with an application to braces. Communications in Contemporary Mathematics, 2050010
https://doi.org/10.1142/s0219199720500108, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa53070

Holl Ymchwil

Erthyglau Cylchgronau

Breaz, S., Brzezinski, T., Rybołowicz, B., & Saracco, P. (2024). Heaps of modules and affine spaces. Annali di Matematica Pura ed Applicata (1923 -), 203(1), 403-445.
https://doi.org/10.1007/s10231-023-01369-0, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa64523
Brzezinski, T. (2023). On the algebra of elliptic curves. Proceedings of the Edinburgh Mathematical Society, 66(2), 548-556.
https://doi.org/10.1017/s0013091523000275, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa63749
Brzezinski, T., Rybołowicz, B., & Saracco, P. (2022). On functors between categories of modules over trusses. Journal of Pure and Applied Algebra, 226(11), 107091
https://doi.org/10.1016/j.jpaa.2022.107091, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa59386
Brzezinski, T., Mereta, S., & Rybolowicz, B. (2022). From pre-trusses to skew braces. Publicacions Matemàtiques, 66(2), 683-714.
https://doi.org/10.5565/publmat6622206, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa56171
Andruszkiewicz, R., Brzezinski, T., & Rybołowicz, B. (2022). Ideal ring extensions and trusses. Journal of Algebra, 600, 237-278.
https://doi.org/10.1016/j.jalgebra.2022.01.038, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa60087
Breaz, S. & Brzezinski, T. (2021). The Baer–Kaplansky Theorem for all abelian groups and modules. Bulletin of Mathematical Sciences, 12(01), 1-12.
https://doi.org/10.1142/s1664360721500053, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa56478
Brzezinski, T. & Szymański, W. (2021). An algebraic framework for noncommutative bundles with homogeneous fibres. Algebra & Number Theory, 15(1), 217-240.
https://doi.org/10.2140/ant.2021.15.217, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa54834
Brzezinski, T. & Rybołowicz, B. (2020). Modules Over Trusses vs Modules Over Rings: Direct Sums and Free Modules. Algebras and Representation Theory
https://doi.org/10.1007/s10468-020-10008-8, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa57814
Brzezinski, T. (2020). Trusses: Paragons, ideals and modules. Journal of Pure and Applied Algebra, 224(6), 106258
https://doi.org/10.1016/j.jpaa.2019.106258, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa52083
http://dx.doi.org/10.1016/j.jpaa.2019.106258
Brzezinski, T., Koenig, S., & Külshammer, J. (2020). From quasi‐hereditary algebras with exact Borel subalgebras to directed bocses. Bulletin of the London Mathematical Society, 52(2), 367-378.
https://doi.org/10.1112/blms.12331, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa53009
Brzezinski, T. & Rybolowicz, B. (2020). Congruence classes and extensions of rings with an application to braces. Communications in Contemporary Mathematics, 2050010
https://doi.org/10.1142/s0219199720500108, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa53070
Brzezinski, T., Gaunt, J., & Schenkel, A. (2020). On the Relationship between Classical and Deformed Hopf Fibrations. Symmetry, Integrability and Geometry: Methods and Applications, 16(008)
https://doi.org/10.3842/sigma.2020.008, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa53623
Brzeziński, T., Dąbrowski, L., Sitarz, A., & Brzezinski, T. (2019). On twisted reality conditions. Letters in Mathematical Physics, 109, 643-659.
https://doi.org/10.1007/s11005-018-1120-x, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa41070
Brzezinski, T. & Szymanski, W. (2019). The Quantum Flag Manifold SUq(3)/T2 as an Example of a Noncommutative Sphere Bundle. arXiv
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa52508
https://arxiv.org/abs/1906.04083
Brzezinski, T. (2018). Towards semi-trusses. Rev. Roumaine Math. Pures Appl, LXIII(2/2018), 75-89.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa38308
http://imar.ro/journals/Revue_Mathematique/php/2018/Rrc18_2.php
Brzeziński, T., Lomp, C., & Brzezinski, T. (2018). Differential smoothness of skew polynomial rings. Journal of Pure and Applied Algebra, 222(9), 2413-2426.
https://doi.org/10.1016/j.jpaa.2017.09.020, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa34892
Brzezinski, T. (2018). Trusses: Between braces and rings. Transactions of the American Mathematical Society, 372(6), 4149-4176.
https://doi.org/10.1090/tran/7705, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa44243
http://dx.doi.org/10.1090/tran/7705
Brzeziński, T., Szymański, W., & Brzezinski, T. (2018). The $C^*$-algebras of quantum lens and weighted projective spaces. Journal of Noncommutative Geometry, 12(1), 195-215.
https://doi.org/10.4171/JNCG/274, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa37050
Almulhem, M., Brzeziński, T., & Brzezinski, T. (2018). Skew derivations on generalized Weyl algebras. Journal of Algebra, 493, 194-235.
https://doi.org/10.1016/j.jalgebra.2017.09.018, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa35456
Brzezinski, T. & Sitarz, A. (2017). Smooth geometry of the noncommutative pillow, cones and lens spaces. Journal of Noncommutative Geometry, 11(2), 413-449.
https://doi.org/10.4171/JNCG/11-2-1, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa22144
http://www.ems-ph.org/doi/10.4171/JNCG/11-2-1
Brzezinski, T. (2017). Curved Rota-Baxter systems. Bulletin of the Belgian Mathematical Society - Simon Stevin, 23(5), 713-720.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa27393
http://projecteuclid.org/euclid.bbms/1483671622
Brzeziński, T. & Brzezinski, T. (2016). Circle and Line Bundles Over Generalized Weyl Algebras. Algebras and Representation Theory, 19(1), 57-69.
https://doi.org/10.1007/s10468-015-9562-7, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa22634
Brzeziński, T., Ciccoli, N., Dąbrowski, L., Sitarz, A., & Brzezinski, T. (2016). Twisted Reality Condition for Dirac Operators. Mathematical Physics, Analysis and Geometry, 19(3)
https://doi.org/10.1007/s11040-016-9219-8, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa28994
http://arxiv.org/abs/1601.07404
Brzeziński, T. & Brzezinski, T. (2016). Rota–Baxter systems, dendriform algebras and covariant bialgebras. Journal of Algebra, 460, 1-25.
https://doi.org/10.1016/j.jalgebra.2016.04.018, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa27394
Brzezinski, T. (2016). Noncommutative Differential Geometry of Generalized Weyl Algebras. Symmetry, Integrability and Geometry: Methods and Applications, 12, 059
https://doi.org/10.3842/SIGMA.2016.059, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa28992
http://www.emis.de/journals/SIGMA/2016/059/
Brzeziński, T., Fairfax, S., & Brzezinski, T. (2015). Notes on quantum weighted projective spaces and multidimensional teardrops. Journal of Geometry and Physics, 93, 1-10.
https://doi.org/10.1016/j.geomphys.2015.03.001, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa20561
http://arxiv.org/abs/1412.3586
Brzezinski, T. (2015). Differential smoothness of affine Hopf algebras of Gelfand-Kirillov dimension two. COLLOQUIUM MATHEMATICUM, 139(1), 111-119.
https://doi.org/10.4064/cm139-1-6, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa20514
http://arxiv.org/abs/1412.6669
Beggs, E., Brzeziński, T., & Brzezinski, T. (2014). Line bundles and the Thom construction in noncommutative geometry. Journal of Noncommutative Geometry, 8(1), 61-105.
https://doi.org/10.4171/JNCG/149, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa13888
http://www.ems-ph.org/journals/journal.php?jrn=JNCG
Brzeziński, T., Fairfax, S., & Brzezinski, T. (2014). Weighted Circle Actions on the Heegaard Quantum Sphere. Letters in Mathematical Physics, 104(2), 195-215.
https://doi.org/10.1007/s11005-013-0664-z, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa20518
http://arxiv.org/abs/1305.5942
Brzezinski, T. (2014). Complex geometry of quantum cones. Fortschritte der Physik, 62(9-10), 875-880.
https://doi.org/10.1002/prop.201400051, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa20516
http://arxiv.org/abs/1406.2517
Brzeziński, T. & Brzezinski, T. (2014). On the Smoothness of the Noncommutative Pillow and Quantum Teardrops. Symmetry, Integrability and Geometry: Methods and Applications
https://doi.org/10.3842/SIGMA.2014.015, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa20517
Beggs, E., Brzeziński, T., Beggs, E., & Brzezinski, T. (2014). Noncommutative differential operators, Sobolev spaces and the centre of a category. Journal of Pure and Applied Algebra, 218(1), 1-17.
https://doi.org/10.1016/j.jpaa.2013.04.006, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa20867
Brzeziński, T. & Brzezinski, T. (2013). Curved differential graded algebras and corings. , 20
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39803
http://www.scopus.com/inward/record.url?eid=2-s2.0-84896328857&partnerID=MN8TOARS
Brzeziński, T., Zieliński, B., & Brzezinski, T. (2012). Quantum principal bundles over quantum real projective spaces. Journal of Geometry and Physics, 62(5), 1097-1107.
https://doi.org/10.1016/j.geomphys.2011.12.008, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa7441
Brzezinski, T. (2012). R-smash products of Hopf quasigroups. Arabian Journal of Mathematics, 1, 39-46.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa8010
Brzezinski, T. (2012). Actions of Hopf quasigroups. Communications in Algebra, 40(2), 681-696.
https://doi.org/10.1080/00927872.2010.535588, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa8009
Brzeziński, T. & Brzezinski, T. (2012). A note on flat noncommutative connections. Banach Center Publications, 98, 43-53.
https://doi.org/10.4064/bc98-0-2, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa8017
Brzeziński, T., Fairfax, S., & Brzezinski, T. (2012). Quantum Teardrops. Communications in Mathematical Physics, 316(1), 151-170.
https://doi.org/10.1007/s00220-012-1580-2, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa8018
Brzeziński, T., Zieliński, B., & Brzezinski, T. (2012). Quantum principal bundles over quantum real projective spaces. Journal of Geometry and Physics, 62(5), 1097-1107.
https://doi.org/10.1016/j.geomphys.2011.12.008, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa13418
Brzeziński, T., Fairfax, S., & Brzezinski, T. (2012). Bundles over Quantum Real Weighted Projective Spaces. Axioms, 1(2), 201-225.
https://doi.org/10.3390/axioms1020201, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa13419
Brzezinski, T. (2012). Bundles over quantum projective spaces. Proceedings of Science
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa13421
Brzezinski, T. (2011). Divergences on projective modules and non-commutative integrals. Int J Geom Methods Mod Phys, 8, 885-896.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1049
Brzeziński, T., Marquez, A., Vercruysse, J., & Brzezinski, T. (2011). The Eilenberg-Moore Category and a Beck-type Theorem for a Morita Context. Applied Categorical Structures, 19(5), 821-858.
https://doi.org/10.1007/s10485-009-9217-0, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa7443
BRZEZIŃSKI, T. & Brzezinski, T. (2011). DIVERGENCES ON PROJECTIVE MODULES AND NON-COMMUTATIVE INTEGRALS. International Journal of Geometric Methods in Modern Physics, 08(04), 885-896.
https://doi.org/10.1142/S0219887811005440, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa7446
Brzeziński, T. & Brzezinski, T. (2011). Non-commutative orders. A preliminary study. Acta Physica Polonica B Proceedings Supplement, 4(3), 273-286.
https://doi.org/10.5506/APhysPolBSupp.4.273, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa7448
http://th-www.if.uj.edu.pl/acta/sup4/abs/s4p0273.htm
Brzeziński, T., Vazquez-Marquez, A., & Brzezinski, T. (2011). Internal Kleisli categories. Journal of Pure and Applied Algebra, 215(9), 2135-2147.
https://doi.org/10.1016/j.jpaa.2010.12.003, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa7449
Brzeziński, T., Kaoutit, L., Lomp, C., & Brzezinski, T. (2010). Non-commutative integral forms and twisted multi-derivations. Journal of Noncommutative Geometry, 4(2), 281-312.
https://doi.org/10.4171/JNCG/56, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1048
Brzeziński, T. & Brzezinski, T. (2010). Integral calculus on Eq(2). Symmetry, Integrability and Geometry: Methods and Applications
https://doi.org/10.3842/SIGMA.2010.040, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa7447
Brzeziński, T., Kaoutit, L., Lomp, C., & Brzezinski, T. (2010). Non-commutative integral forms and twisted multi-derivations. Journal of Noncommutative Geometry, 281-312.
https://doi.org/10.4171/JNCG/56, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa8012
Brzezinski, T. (2010). Hopf modules and the fundamental theorem for Hopf (co)quasigroups. Int. Electron. J. Algebra, 8, 114-1128.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa8014
Brzezinski, T. (2010). On synthetic interpretation of quantum principal bundles. AJSE D - Mathematics, 35(1D), 13-27.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa8015
Böhm, G., Brzeziński, T., & Brzezinski, T. (2009). Corrigendum to Cleft Extensions of Hopf Algebroids. Applied Categorical Structures, 17(6), 613-620.
https://doi.org/10.1007/s10485-008-9168-x, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39805
http://www.scopus.com/inward/record.url?eid=2-s2.0-71449095273&partnerID=MN8TOARS
Brzeziński, T., Vercruysse, J., & Brzezinski, T. (2009). Bimodule herds. Journal of Algebra, 321(9), 2670-2704.
https://doi.org/10.1016/j.jalgebra.2009.01.020, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1050
Böhm, G., Brzeziński, T., Wisbauer, R., & Brzezinski, T. (2009). Monads and comonads on module categories. Journal of Algebra, 322(5), 1719-1747.
https://doi.org/10.1016/j.jalgebra.2009.06.003, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1051
Beggs, E., Brzeziński, T., & Brzezinski, T. (2008). An Explicit Formula for a Strong Connection. Applied Categorical Structures, 16(1-2), 57-63.
https://doi.org/10.1007/s10485-007-9087-2, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa7194
Ardizzoni, A., Brzeziński, T., Menini, C., & Brzezinski, T. (2008). Formally smooth bimodules. Journal of Pure and Applied Algebra, 212(5)-1085.
https://doi.org/10.1016/j.jpaa.2007.09.004, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa15599
BRZEZIŃSKI, T. & Brzezinski, T. (2008). NON-COMMUTATIVE CONNECTIONS OF THE SECOND KIND. Journal of Algebra and Its Applications, 07(05), 557-573.
https://doi.org/10.1142/S0219498808002977, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa7445
Brzeziński, T. & Brzezinski, T. (2008). Descent Cohomology and Corings. Communications in Algebra, 36(5), 1894-1900.
https://doi.org/10.1080/00927870801941523, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa7444
Böhm, G., Brzeziński, T., & Brzezinski, T. (2007). Pre-torsors and equivalences. Journal of Algebra, 317(2)-580.
https://doi.org/10.1016/j.jalgebra.2007.08.023, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa15600
Brzeziński, T., Turner, R., Wrightson, A., & Brzezinski, T. (2006). The Structure of Weak Coalgebra-Galois Extensions. Communications in Algebra, 34(4), 1489-1519.
https://doi.org/10.1080/00927870500455056, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39808
http://www.scopus.com/inward/record.url?eid=2-s2.0-33645758450&partnerID=MN8TOARS
Brzeziński, T., El Kaoutit, L., Gómez-Torrecillas, J., & Brzezinski, T. (2006). The bicategories of corings. Journal of Pure and Applied Algebra, 205(3), 510-541.
https://doi.org/10.1016/j.jpaa.2005.07.013, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39807
http://www.scopus.com/inward/record.url?eid=2-s2.0-33644775572&partnerID=MN8TOARS
Böhm, G., Brzeziński, T., & Brzezinski, T. (2006). Cleft Extensions of Hopf Algebroids. Applied Categorical Structures, 14(5-6), 431-469.
https://doi.org/10.1007/s10485-006-9043-6, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39806
http://www.scopus.com/inward/record.url?eid=2-s2.0-33845310044&partnerID=MN8TOARS
Brzeziński, T., Turner, R., & Brzezinski, T. (2006). The Galois Theory of Matrix C-rings. Applied Categorical Structures, 14(5-6)-501.
https://doi.org/10.1007/s10485-006-9044-5, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa15601
Beggs, E., Brzeziński, T., & Brzezinski, T. (2005). The serre spectral sequence of a noncommutative fibration for de Rham cohomology. Acta Mathematica, 195(2), 155-196.
https://doi.org/10.1007/BF02588079, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1609
Brzeziński, T., Wrightson, A., & Brzezinski, T. (2005). COMPLETE COVERINGS AND GALOIS CORINGS. International Journal of Geometric Methods in Modern Physics, 2(05), 751-757.
https://doi.org/10.1142/S0219887805000788, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39810
http://www.scopus.com/inward/record.url?eid=2-s2.0-33746325798&partnerID=MN8TOARS
Brzeziński, T. & Brzezinski, T. (2005). A note on coring extensions. , 51
https://doi.org/10.1007/BF02824821, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39809
http://www.scopus.com/inward/record.url?eid=2-s2.0-33750966851&partnerID=MN8TOARS
Brzeziński, T. & Brzezinski, T. (2005). Galois comodules. Journal of Algebra, 290(2), 503-537.
https://doi.org/10.1016/j.jalgebra.2005.05.009, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1614
Bohm, G. & Brzezinski, T. (2005). Strong connections and the relative Chern-Galois character for corings. International Mathematics Research Notices, 42, 2579-2625.
https://doi.org/10.1155/IMRN.2005.2579, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1615
Brzeziński, T., Hajac, P., & Brzezinski, T. (2004). The Chern–Galois character. Comptes Rendus Mathematique, 338(2), 113-116.
https://doi.org/10.1016/j.crma.2003.11.009, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39813
http://www.scopus.com/inward/record.url?eid=2-s2.0-0742302577&partnerID=MN8TOARS
Brzeziński, T., Da̧browski, L., Zieliński, B., & Brzezinski, T. (2004). Hopf fibration and monopole connection over the contact quantum spheres. Journal of Geometry and Physics, 50(1-4), 345-359.
https://doi.org/10.1016/j.geomphys.2003.09.009, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39812
http://www.scopus.com/inward/record.url?eid=2-s2.0-17544402516&partnerID=MN8TOARS
Brzeziński, T. & Brzezinski, T. (2003). Towers of corings. , 31
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39817
http://www.scopus.com/inward/record.url?eid=2-s2.0-0037950266&partnerID=MN8TOARS
Brzeziński, T., Gómez-Torrecillas, J., & Brzezinski, T. (2003). On Comatrix Corings and Bimodules. K-Theory, 29(2), 101-115.
https://doi.org/10.1023/B:KTHE.0000006751.77914.50, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39815
http://www.scopus.com/inward/record.url?eid=2-s2.0-3543011392&partnerID=MN8TOARS
Brzeziński, T. & Brzezinski, T. (2002). The structure of corings: Induction functors, Maschke-type theorem, and Frobenius and Galois-type properties. Algebras and Representation Theory, 5(4), 389-410.
https://doi.org/10.1023/A:1020139620841, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39819
http://www.scopus.com/inward/record.url?eid=2-s2.0-0036795308&partnerID=MN8TOARS
Brzeziński, T., Caenepeel, S., Militaru, G., & Brzezinski, T. (2002). Doi–Koppinen modules for quantum groupoids. Journal of Pure and Applied Algebra, 175(1-3), 45-62.
https://doi.org/10.1016/S0022-4049(02)00128-7, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39818
http://www.scopus.com/inward/record.url?eid=2-s2.0-0037044678&partnerID=MN8TOARS
Brzeziński, T., Militaru, G., & Brzezinski, T. (2002). Bialgebroids, ×A-Bialgebras and Duality. Journal of Algebra, 251(1), 279-294.
https://doi.org/10.1006/jabr.2001.9101, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa1613
Brzeziński, T. & Brzezinski, T. (2001). The Cohomology Structure of an Algebra Entwined with a Coalgebra. Journal of Algebra, 235(1), 176-202.
https://doi.org/10.1006/jabr.2000.8469, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39821
http://www.scopus.com/inward/record.url?eid=2-s2.0-0035217393&partnerID=MN8TOARS
Brzeziński, T. & Brzezinski, T. (2001). DEFORMATION OF ALGEBRA FACTORISATIONS. Communications in Algebra, 29(2), 737-748.
https://doi.org/10.1081/AGB-100001537, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39820
http://www.scopus.com/inward/record.url?eid=2-s2.0-0035606482&partnerID=MN8TOARS
Brzeziński, T., Majid, S., & Brzezinski, T. (2000). Quantum geometry of algebra factorisations and coalgebra bundles. , 213
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39825
http://www.scopus.com/inward/record.url?eid=2-s2.0-0034349407&partnerID=MN8TOARS
Brzeziński, T., Gonera, C., & Brzezinski, T. (2000). Noncommutative 4-spheres based on all Podleś 2-spheres and beyond. , 54
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39824
http://www.scopus.com/inward/record.url?eid=2-s2.0-0011288326&partnerID=MN8TOARS
Brzeziński, T. & Brzezinski, T. (2000). Frobenius properties and maschke-type theorems for entwined modules. , 128
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39823
http://www.scopus.com/inward/record.url?eid=2-s2.0-26844448734&partnerID=MN8TOARS
Brzeziński, T., Gonera, C., Kosiński, P., Maślanka, P., & Brzezinski, T. (2000). A note on the action-angle variables for the rational Calogero–Moser system. Physics Letters A, 268(3), 178-180.
https://doi.org/10.1016/S0375-9601(00)00173-0, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39822
http://www.scopus.com/inward/record.url?eid=2-s2.0-0034629886&partnerID=MN8TOARS
Brzeziński, T., Gonera, C., Maślanka, P., & Brzezinski, T. (1999). On the equivalence of the rational Calogero-Moser system to free particles. , 254
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39828
http://www.scopus.com/inward/record.url?eid=2-s2.0-0043282197&partnerID=MN8TOARS
Brzeziński, T. & Brzezinski, T. (1999). On modules associated to coalgebra Galois extensions. , 215
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39827
http://www.scopus.com/inward/record.url?eid=2-s2.0-0033130419&partnerID=MN8TOARS
Brzeziński, T., Hajac, P., & Brzezinski, T. (1999). Coalgebra extensions and algebra coextensions of Galois type. , 27
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39826
http://www.scopus.com/inward/record.url?eid=2-s2.0-0033240710&partnerID=MN8TOARS
Brzeziński, T., Majid, S., & Brzezinski, T. (1998). Quantum differentials and the g-monopole revisited. , 54
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39830
http://www.scopus.com/inward/record.url?eid=2-s2.0-0032206103&partnerID=MN8TOARS
Brzezínski, T., Majid, S., & Brzezinski, T. (1998). Coalgebra bundles. , 191
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39829
http://www.scopus.com/inward/record.url?eid=2-s2.0-0039243646&partnerID=MN8TOARS
Brzeziński, T. & Brzezinski, T. (1997). Quantum homogeneous spaces and coalgebra bundles. , 40
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39833
http://www.scopus.com/inward/record.url?eid=2-s2.0-0031256565&partnerID=MN8TOARS
Brzeziński, T., Merabet, H., & Brzezinski, T. (1997). Nahm's equations and root systems. , 47
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39832
http://www.scopus.com/inward/record.url?eid=2-s2.0-0039377472&partnerID=MN8TOARS
Brzeziński, T. & Brzezinski, T. (1997). Crossed products by a coalgebra. , 25
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39831
http://www.scopus.com/inward/record.url?eid=2-s2.0-0344238605&partnerID=MN8TOARS
Brzeziński, T. & Brzezinski, T. (1996). Translation map in quantum principal bundles. Journal of Geometry and Physics, 20(4), 349-370.
https://doi.org/10.1016/S0393-0440(96)00003-4, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39836
http://www.scopus.com/inward/record.url?eid=2-s2.0-0030295845&partnerID=MN8TOARS
Brzeziński, T. & Brzezinski, T. (1996). Separation of variables and vacuum structure of N = 2 SUSY QCD. Physics Letters B, 383(3), 294-300.
https://doi.org/10.1016/0370-2693(96)00757-5, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39835
http://www.scopus.com/inward/record.url?eid=2-s2.0-13544265780&partnerID=MN8TOARS
Brzeziński, T. & Brzezinski, T. (1996). Quantum homogeneous spaces as quantum quotient spaces. Journal of Mathematical Physics, 37(5), 2388-2399.
https://doi.org/10.1063/1.531517, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39834
http://www.scopus.com/inward/record.url?eid=2-s2.0-0030528306&partnerID=MN8TOARS
Brzezinski, T., Katriel, J., & Brzezinski, T. (1995). Representation-theoretic derivation of the Temperley-Lieb-Martin algebras. Journal of Physics A: Mathematical and General, 28(18), 5305-5312.
https://doi.org/10.1088/0305-4470/28/18/019, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39838
http://www.scopus.com/inward/record.url?eid=2-s2.0-21844493379&partnerID=MN8TOARS
Brzeziński, T., Majid, S., & Brzezinski, T. (1995). Quantum group Gauge theory on quantum spaces. Communications in Mathematical Physics, 167(1), 235-235.
https://doi.org/10.1007/BF02099359, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39837
http://www.scopus.com/inward/record.url?eid=2-s2.0-33749153291&partnerID=MN8TOARS
Brzeziński, T., Macfarlane, A., & Brzezinski, T. (1994). On integrable models related to the osp(1,2) Gaudin algebra. , 35
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39840
http://www.scopus.com/inward/record.url?eid=2-s2.0-21344481311&partnerID=MN8TOARS
Brzeziński, T. & Brzezinski, T. (1994). Dynamical r-matrices and separation of variables: The generalised Calogero - Moser model. , 325
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39839
http://www.scopus.com/inward/record.url?eid=2-s2.0-0242609553&partnerID=MN8TOARS
Brzeziński, T. & Brzezinski, T. (1993). Remarks on bicovariant differential calculi and exterior Hopf algebras. Letters in Mathematical Physics, 27(4), 287-300.
https://doi.org/10.1007/BF00777376, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39845
http://www.scopus.com/inward/record.url?eid=2-s2.0-0002601531&partnerID=MN8TOARS
Brzezinski, T. & Brzezinski, T. (1993). Quantum group related to the space of differential operators on the quantum hyperplane. Journal of Physics A: Mathematical and General, 26(4), 905-911.
https://doi.org/10.1088/0305-4470/26/4/017, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39844
http://www.scopus.com/inward/record.url?eid=2-s2.0-36149035657&partnerID=MN8TOARS
Brzeziński, T., Majid, S., & Brzezinski, T. (1993). Quantum group gauge theory on quantum spaces. Communications in Mathematical Physics, 157(3), 591-638.
https://doi.org/10.1007/BF02096884, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39843
http://www.scopus.com/inward/record.url?eid=2-s2.0-25444450141&partnerID=MN8TOARS
Brzeziński, T., Majid, S., & Brzezinski, T. (1993). Quantum group gauge theory on classical spaces. , 298
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39842
http://www.scopus.com/inward/record.url?eid=2-s2.0-0010951840&partnerID=MN8TOARS
Brzeziński, T., Egusquiza, I., Macfarlane, A., & Brzezinski, T. (1993). Generalised harmonic oscillator systems and their Fock space description. , 311
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39841
http://www.scopus.com/inward/record.url?eid=2-s2.0-0001700910&partnerID=MN8TOARS
Brzezinski, T., Rembielinski, J., & Brzezinski, T. (1992). q-integrals on the quantum complex plane. Journal of Physics A: Mathematical and General, 25(7), 1945-1951.
https://doi.org/10.1088/0305-4470/25/7/033, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39848
http://www.scopus.com/inward/record.url?eid=2-s2.0-0039299226&partnerID=MN8TOARS
Brzeziński, T., Da̧browski, H., Rembieliński, J., & Brzezinski, T. (1992). On the quantum differential calculus and the quantum holomorphicity. , 33
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39847
http://www.scopus.com/inward/record.url?eid=2-s2.0-36449000417&partnerID=MN8TOARS
Brzeziński, T., Majid, S., & Brzezinski, T. (1992). A class of bicovariant differential calculi on hopf algebras. Letters in Mathematical Physics, 26(1), 67-78.
https://doi.org/10.1007/BF00420519, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39846
http://www.scopus.com/inward/record.url?eid=2-s2.0-0010070262&partnerID=MN8TOARS

Llyfrau Awdurol

Brzezinski, T. & Wisbauer, R. (2003). Corings and Comodules Cambridge University Press.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa20512

Penodau Llyfrau

Brzezinski, T. (2023). Homothetic Rota–Baxter Systems and Dyck$$^m$$-Algebras. Springer Proceedings in Mathematics & Statistics (pp. 103-110). Springer Nature Singapore
https://doi.org/10.1007/978-981-19-4751-3_7, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa62800
http://dx.doi.org/10.1007/978-981-19-4751-3_7
Brzezinski, T. & Szymański, W. (2019). On the quantum flag manifold SUq(3)/T2. Trends in Mathematics (pp. 129-139). Springer International Publishing
https://doi.org/10.1007/978-3-030-34072-8_13, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa53086
Brzeziński, T. & Brzezinski, T. (2012). A note on flat noncommutative connections. Banach Center Publications (pp. 43-53).
https://doi.org/10.4064/bc98-0-2, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa20521
Brzezinski, T. (2011). Hopf-cyclic homology with contramodule coefficients.. Quantum Groups and Noncommutative Spaces (pp. 1-9). Vieweg+Teubner Verlag
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa8013
Brzeziński, T. & Brzezinski, T. (2009). Comodules and Corings. Handbook of Algebra - Volume 6 (pp. 237-318).
https://doi.org/10.1016/S1570-7954(08)00206-4, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa7442
Brzezinski, T. & Hajac, P. (2009). Galois-type extensions and equivariant projectivity. Quantum Symmetry in Noncommutative Geometry European Mathematical Society Publishing House
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa8011
Brzezinski, T. (2008). Notes on formal smoothness. Modules and Comodules (pp. 113-124). Birkhauser
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa8016

Cyfraniadau Cynadleddau

Brzezinski, T. (2022). Lie trusses and heaps of Lie affebras. In Proceedings of Corfu Summer Institute 2021 "School and Workshops on Elementary Particle Physics and Gravity" — PoS(CORFU2021)Sissa Medialab.
https://doi.org/10.22323/1.406.0307, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa62196
Brzeziński, T. & Brzezinski, T. (2011). Circle actions on a quantum Seifert manifold.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39804
http://www.scopus.com/inward/record.url?eid=2-s2.0-84883531994&partnerID=MN8TOARS
Brzeziński, T., Sitarz, A., & Brzezinski, T. (2003). Dirac monopoles from the Matsumoto non-commutative spheres.
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa39814
http://www.scopus.com/inward/record.url?eid=2-s2.0-4944266661&partnerID=MN8TOARS

Goruchwyliaeth

Ore extensions of trusses (cyfredol)

PhD

Goruchwyliwr arall: Dr Nelly Villamizar
Applications of Chern-Simons theories to integrable models (cyfredol)

PhD

Goruchwyliwr arall: Prof Daniel Thompson
Provisional Title: Trusses and Applications of Trusses (cyfredol)

PhD

Goruchwyliwr arall: Prof Grigory Garkusha

Goruchwyliwr arall: Prof Grigory Garkusha
Submanifolds, Fibre Bundles, and Cofibrations in Noncommutative Differential Geometry (dyfarnwyd 2024)

PhD

Goruchwyliwr arall: Dr Edwin Beggs
Applications of Topological Data Analysis to Statistical Physics and Quantum Field Theory (dyfarnwyd 2022)

PhD

Goruchwyliwr arall: Prof Jeffrey Giansiracusa

Goruchwyliwr arall: Prof Biagio Lucini
Higher rank tropicalisation (dyfarnwyd 2024)

PhD

Goruchwyliwr arall: Dr Nelly Villamizar

Goruchwyliwr arall: Prof Jeffrey Giansiracusa

Goruchwyliwr arall: Dr Edwin Beggs
Generalisations of Tropical Geometry over Hyperfields. (dyfarnwyd 2022)

PhD

Goruchwyliwr arall: Prof Jeffrey Giansiracusa

Goruchwyliwr arall: Dr Edwin Beggs
A GENERAL FRAMEWORK FOR TROPICAL DIFFERENTIAL EQUATIONS (dyfarnwyd 2022)

PhD

Goruchwyliwr arall: Prof Grigory Garkusha

Goruchwyliwr arall: Prof Jeffrey Giansiracusa

Modiwlau a Addysgir

MA-322 Topology

This module explores the topological approach to continuity and the study of objects via their topological structure
MA-E01 Year Abroad

Students are required to select appropriate maths modules. The modules chosen are detailed within a Learning Agreement which must be approved by the Study Abroad Co-ordinator at Swansea University before the student leaves Swansea.
MA-M22 Topology

This module explores the topological approach to continuity and the study of objects via their topological structure

Yr Athro Tomasz Brzezinski

Cyfeiriad ebost

Dolenni Ymchwil

Trosolwg

Meysydd Arbenigedd

Cyhoeddiadau

Uchafbwyntiau Ymchwil

Holl Ymchwil

Erthyglau Cylchgronau

Llyfrau Awdurol

Penodau Llyfrau

Cyfraniadau Cynadleddau

Goruchwyliaeth

Ore extensions of trusses (cyfredol)

Applications of Chern-Simons theories to integrable models (cyfredol)

Provisional Title: Trusses and Applications of Trusses (cyfredol)

Submanifolds, Fibre Bundles, and Cofibrations in Noncommutative Differential Geometry (dyfarnwyd 2024)

Applications of Topological Data Analysis to Statistical Physics and Quantum Field Theory (dyfarnwyd 2022)

Higher rank tropicalisation (dyfarnwyd 2024)

Generalisations of Tropical Geometry over Hyperfields. (dyfarnwyd 2022)

A GENERAL FRAMEWORK FOR TROPICAL DIFFERENTIAL EQUATIONS (dyfarnwyd 2022)

Modiwlau a Addysgir

MA-322 Topology

MA-E01 Year Abroad

MA-M22 Topology