Professor Tomasz Brzezinski

Publications

Journal Articles

  1. & Smooth geometry of the noncommutative pillow, cones and lens spaces. Journal of Noncommutative Geometry 11(2), 413-449.
  2. Curved Rota-Baxter systems. Bulletin of the Belgian Mathematical Society - Simon Stevin 23
  3. & Skew derivations on generalized Weyl algebras. Journal of Algebra
  4. & Differential smoothness of skew polynomial rings. Journal of Pure and Applied Algebra
  5. Rota–Baxter systems, dendriform algebras and covariant bialgebras. Journal of Algebra 460, 1-25.
  6. Noncommutative Differential Geometry of Generalized Weyl Algebras. Symmetry, Integrability and Geometry: Methods and Applications 12, 059
  7. Circle and Line Bundles Over Generalized Weyl Algebras. Algebras and Representation Theory 19(1), 57-69.
  8. & Twisted Reality Condition for Dirac Operators. Mathematical Physics, Analysis and Geometry 19(3)
  9. Differential smoothness of affine Hopf algebras of Gelfand-Kirillov dimension two. COLLOQUIUM MATHEMATICUM 139(1), 111-119.
  10. & Notes on quantum weighted projective spaces and multidimensional teardrops. Journal of Geometry and Physics 93, 1-10.
  11. & Noncommutative differential operators, Sobolev spaces and the centre of a category. Journal of Pure and Applied Algebra 218(1), 1-17.
  12. & Line bundles and the Thom construction in noncommutative geometry. Journal of Noncommutative Geometry 8(1), 61-105.
  13. & Weighted Circle Actions on the Heegaard Quantum Sphere. Letters in Mathematical Physics 104(2), 195-215.
  14. On the Smoothness of the Noncommutative Pillow and Quantum Teardrops. Symmetry, Integrability and Geometry: Methods and Applications
  15. Complex geometry of quantum cones. Fortschritte der Physik 62(9-10), 875-880.
  16. & Quantum principal bundles over quantum real projective spaces. Journal of Geometry and Physics 62(5), 1097-1107.
  17. R-smash products of Hopf quasigroups. Arabian Journal of Mathematics 1, 39-46.
  18. Actions of Hopf quasigroups. Communications in Algebra 40(2), 681-696.
  19. A note on flat noncommutative connections. Banach Center Publications 98, 43-53.
  20. & Quantum Teardrops. Communications in Mathematical Physics 316(1), 151-170.
  21. & Quantum principal bundles over quantum real projective spaces. Journal of Geometry and Physics 62(5), 1097-1107.
  22. & Bundles over Quantum Real Weighted Projective Spaces. Axioms 1(2), 201-225.
  23. Bundles over quantum projective spaces. Proceedings of Science
  24. Divergences on projective modules and non-commutative integrals. Int J Geom Methods Mod Phys 8, 885-896.
  25. & The Eilenberg-Moore Category and a Beck-type Theorem for a Morita Context. Applied Categorical Structures 19(5), 821-858.
  26. DIVERGENCES ON PROJECTIVE MODULES AND NON-COMMUTATIVE INTEGRALS. International Journal of Geometric Methods in Modern Physics 08(04), 885-896.
  27. Non-commutative orders. A preliminary study. Acta Physica Polonica B Proceedings Supplement 4(3), 273-286.
  28. & Internal Kleisli categories. Journal of Pure and Applied Algebra 215(9), 2135-2147.
  29. & Non-commutative integral forms and twisted multi-derivations. Journal of Noncommutative Geometry 4(2), 281-312.
  30. Integral calculus on Eq(2). Symmetry, Integrability and Geometry: Methods and Applications
  31. & Non-commutative integral forms and twisted multi-derivations. Journal of Noncommutative Geometry, 281-312.
  32. Hopf modules and the fundamental theorem for Hopf (co)quasigroups. Int. Electron. J. Algebra 8, 114-1128.
  33. On synthetic interpretation of quantum principal bundles. AJSE D - Mathematics 35(1D), 13-27.
  34. & Bimodule herds. Journal of Algebra 321(9), 2670-2704.
  35. & Monads and comonads on module categories. Journal of Algebra 322(5), 1719-1747.
  36. & Formally smooth bimodules. Journal of Pure and Applied Algebra 212(5)-1085.
  37. & An Explicit Formula for a Strong Connection. Applied Categorical Structures 16(1-2)-63.
  38. NON-COMMUTATIVE CONNECTIONS OF THE SECOND KIND. Journal of Algebra and Its Applications 07(05), 557-573.
  39. Descent Cohomology and Corings. Communications in Algebra 36(5), 1894-1900.
  40. & Pre-torsors and equivalences. Journal of Algebra 317(2)-580.
  41. & The Galois Theory of Matrix C-rings. Applied Categorical Structures 14(5-6)-501.
  42. Galois comodules. Journal of Algebra 290(2), 503-537.
  43. & Strong connections and the relative Chern-Galois character for corings. International Mathematics Research Notices 42, 2579-2625.
  44. & Bialgebroids, ×A-Bialgebras and Duality. Journal of Algebra 251(1), 279-294.

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.