Professor Tomasz Brzezinski

Publications

Journal Articles

  1. Towards semi-trusses. Rev. Roumaine Math. Pures Appl LXIII(2/2018)
  2. & The C*-algebras of quantum lens and weighted projective spaces. Journal of Noncommutative Geometry
  3. & Skew derivations on generalized Weyl algebras. Journal of Algebra 493, 194-235.
  4. & Differential smoothness of skew polynomial rings. Journal of Pure and Applied Algebra 222(9), 2413-2426.
  5. & Smooth geometry of the noncommutative pillow, cones and lens spaces. Journal of Noncommutative Geometry 11(2), 413-449.
  6. Curved Rota-Baxter systems. Bulletin of the Belgian Mathematical Society - Simon Stevin 23
  7. Rota–Baxter systems, dendriform algebras and covariant bialgebras. Journal of Algebra 460, 1-25.
  8. Noncommutative Differential Geometry of Generalized Weyl Algebras. Symmetry, Integrability and Geometry: Methods and Applications 12, 059
  9. Circle and Line Bundles Over Generalized Weyl Algebras. Algebras and Representation Theory 19(1), 57-69.
  10. & Twisted Reality Condition for Dirac Operators. Mathematical Physics, Analysis and Geometry 19(3)
  11. & Notes on quantum weighted projective spaces and multidimensional teardrops. Journal of Geometry and Physics 93, 1-10.
  12. Differential smoothness of affine Hopf algebras of Gelfand-Kirillov dimension two. COLLOQUIUM MATHEMATICUM 139(1), 111-119.
  13. & Noncommutative differential operators, Sobolev spaces and the centre of a category. Journal of Pure and Applied Algebra 218(1), 1-17.
  14. & Line bundles and the Thom construction in noncommutative geometry. Journal of Noncommutative Geometry 8(1), 61-105.
  15. & Weighted Circle Actions on the Heegaard Quantum Sphere. Letters in Mathematical Physics 104(2), 195-215.
  16. On the Smoothness of the Noncommutative Pillow and Quantum Teardrops. Symmetry, Integrability and Geometry: Methods and Applications
  17. Complex geometry of quantum cones. Fortschritte der Physik 62(9-10), 875-880.
  18. Curved differential graded algebras and corings. 20
  19. & Quantum principal bundles over quantum real projective spaces. Journal of Geometry and Physics 62(5), 1097-1107.
  20. R-smash products of Hopf quasigroups. Arabian Journal of Mathematics 1, 39-46.
  21. Actions of Hopf quasigroups. Communications in Algebra 40(2), 681-696.
  22. A note on flat noncommutative connections. Banach Center Publications 98, 43-53.
  23. & Quantum Teardrops. Communications in Mathematical Physics 316(1), 151-170.
  24. & Quantum principal bundles over quantum real projective spaces. Journal of Geometry and Physics 62(5), 1097-1107.
  25. & Bundles over Quantum Real Weighted Projective Spaces. Axioms 1(2), 201-225.
  26. Bundles over quantum projective spaces. Proceedings of Science
  27. Divergences on projective modules and non-commutative integrals. Int J Geom Methods Mod Phys 8, 885-896.
  28. & The Eilenberg-Moore Category and a Beck-type Theorem for a Morita Context. Applied Categorical Structures 19(5), 821-858.
  29. DIVERGENCES ON PROJECTIVE MODULES AND NON-COMMUTATIVE INTEGRALS. International Journal of Geometric Methods in Modern Physics 08(04), 885-896.
  30. Non-commutative orders. A preliminary study. Acta Physica Polonica B Proceedings Supplement 4(3), 273-286.
  31. & Internal Kleisli categories. Journal of Pure and Applied Algebra 215(9), 2135-2147.
  32. & Non-commutative integral forms and twisted multi-derivations. Journal of Noncommutative Geometry 4(2), 281-312.
  33. Integral calculus on Eq(2). Symmetry, Integrability and Geometry: Methods and Applications
  34. & Non-commutative integral forms and twisted multi-derivations. Journal of Noncommutative Geometry, 281-312.
  35. Hopf modules and the fundamental theorem for Hopf (co)quasigroups. Int. Electron. J. Algebra 8, 114-1128.
  36. On synthetic interpretation of quantum principal bundles. AJSE D - Mathematics 35(1D), 13-27.
  37. & Corrigendum to Cleft Extensions of Hopf Algebroids. Applied Categorical Structures 17(6), 613-620.
  38. & Bimodule herds. Journal of Algebra 321(9), 2670-2704.
  39. & Monads and comonads on module categories. Journal of Algebra 322(5), 1719-1747.
  40. & Formally smooth bimodules. Journal of Pure and Applied Algebra 212(5)-1085.
  41. & An Explicit Formula for a Strong Connection. Applied Categorical Structures 16(1-2)-63.
  42. NON-COMMUTATIVE CONNECTIONS OF THE SECOND KIND. Journal of Algebra and Its Applications 07(05), 557-573.
  43. Descent Cohomology and Corings. Communications in Algebra 36(5), 1894-1900.
  44. & Pre-torsors and equivalences. Journal of Algebra 317(2)-580.
  45. & The Structure of Weak Coalgebra-Galois Extensions. Communications in Algebra 34(4), 1489-1519.
  46. & The bicategories of corings. Journal of Pure and Applied Algebra 205(3), 510-541.
  47. & Cleft Extensions of Hopf Algebroids. Applied Categorical Structures 14(5-6), 431-469.
  48. & The Galois Theory of Matrix C-rings. Applied Categorical Structures 14(5-6)-501.
  49. & The serre spectral sequence of a noncommutative fibration for de Rham cohomology. Acta Mathematica 195(2), 155-196.
  50. & COMPLETE COVERINGS AND GALOIS CORINGS. International Journal of Geometric Methods in Modern Physics 2(05), 751-757.
  51. A note on coring extensions. 51
  52. Galois comodules. Journal of Algebra 290(2), 503-537.
  53. & Strong connections and the relative Chern-Galois character for corings. International Mathematics Research Notices 42, 2579-2625.
  54. & The Chern–Galois character. Comptes Rendus Mathematique 338(2), 113-116.
  55. & Hopf fibration and monopole connection over the contact quantum spheres. Journal of Geometry and Physics 50(1-4), 345-359.
  56. Towers of corings. 31
  57. & On Comatrix Corings and Bimodules. K-Theory 29(2), 101-115.
  58. The structure of corings: Induction functors, Maschke-type theorem, and Frobenius and Galois-type properties. Algebras and Representation Theory 5(4), 389-410.
  59. & Doi–Koppinen modules for quantum groupoids. Journal of Pure and Applied Algebra 175(1-3), 45-62.
  60. & Bialgebroids, ×A-Bialgebras and Duality. Journal of Algebra 251(1), 279-294.
  61. The Cohomology Structure of an Algebra Entwined with a Coalgebra. Journal of Algebra 235(1), 176-202.
  62. DEFORMATION OF ALGEBRA FACTORISATIONS. Communications in Algebra 29(2), 737-748.
  63. & Quantum geometry of algebra factorisations and coalgebra bundles. 213
  64. & Noncommutative 4-spheres based on all Podleś 2-spheres and beyond. 54
  65. Frobenius properties and maschke-type theorems for entwined modules. 128
  66. & A note on the action-angle variables for the rational Calogero–Moser system. Physics Letters A 268(3), 178-180.
  67. & On the equivalence of the rational Calogero-Moser system to free particles. 254
  68. On modules associated to coalgebra Galois extensions. 215
  69. & Coalgebra extensions and algebra coextensions of Galois type. 27
  70. & Quantum differentials and the g-monopole revisited. 54
  71. & Coalgebra bundles. 191
  72. Quantum homogeneous spaces and coalgebra bundles. 40
  73. & Nahm's equations and root systems. 47
  74. Crossed products by a coalgebra. 25
  75. Translation map in quantum principal bundles. Journal of Geometry and Physics 20(4), 349-370.
  76. Separation of variables and vacuum structure of N = 2 SUSY QCD. Physics Letters B 383(3), 294-300.
  77. Quantum homogeneous spaces as quantum quotient spaces. Journal of Mathematical Physics 37(5), 2388-2399.
  78. & Representation-theoretic derivation of the Temperley-Lieb-Martin algebras. Journal of Physics A: Mathematical and General 28(18), 5305-5312.
  79. & Quantum group Gauge theory on quantum spaces. Communications in Mathematical Physics 167(1), 235-235.
  80. Dynamical r-matrices and separation of variables: The generalised Calogero - Moser model. 325
  81. & On integrable models related to the osp(1,2) Gaudin algebra. 35
  82. Remarks on bicovariant differential calculi and exterior Hopf algebras. Letters in Mathematical Physics 27(4), 287-300.
  83. Quantum group related to the space of differential operators on the quantum hyperplane. Journal of Physics A: Mathematical and General 26(4), 905-911.
  84. & Quantum group gauge theory on quantum spaces. Communications in Mathematical Physics 157(3), 591-638.
  85. & Quantum group gauge theory on classical spaces. 298
  86. & Generalised harmonic oscillator systems and their Fock space description. 311
  87. & q-integrals on the quantum complex plane. Journal of Physics A: Mathematical and General 25(7), 1945-1951.
  88. & On the quantum differential calculus and the quantum holomorphicity. 33
  89. & A class of bicovariant differential calculi on hopf algebras. Letters in Mathematical Physics 26(1), 67-78.

Books

  1. & Corings and Comodules. Cambridge University Press.

Book Chapters

  1. A note on flat noncommutative connections. In Banach Center Publications. (pp. 43-53).
  2. Comodules and Corings. In Handbook of Algebra - Volume 6. (pp. 237-318).
  3. & Galois-type extensions and equivariant projectivity. In Quantum Symmetry in Noncommutative Geometry. European Mathematical Society Publishing House.
  4. Hopf-cyclic homology with contramodule coefficients.. In Matilde Marcolli, Deepak Parashar (Ed.), Quantum Groups and Noncommutative Spaces. (pp. 1-9). Vieweg+Teubner Verlag.
  5. Notes on formal smoothness. In Tomasz Brzezinski, José Luis Gomez-Pardo, Ivan Shestakov, Patrick F. Smith (Ed.), Modules and Comodules. (pp. 113-124). Birkhauser.

Conference Contributions

  1. (2011). Circle actions on a quantum Seifert manifold.
  2. & (2003). Dirac monopoles from the Matsumoto non-commutative spheres.