P.M. Sołtan

Published papers

  1. W. Paupa & P.M. Sołtan: Invariants of the quantum graph of the partial trace. Open Systems and Information Dynamics 31 (2024), 2450019-1–2450019-1.
  2. J. Krajczok & P.M. Sołtan: Examples of compact quantum groups with \(\mathsf{L}^{\!\infty}(\mathbb{G})\) a factor. J. Funct. Anal. 286 (2024), 110297-1–110297–57.
  3. A. Chirvasitu, J. Krajczok & P.M. Sołtan: Compact quantum group structures on type-I C*-algebras. J. Noncommut. Geom., 17 (2023) 1129–1143.
  4. A. Bochniak, P. Kasprzak & P.M. Sołtan: Quantum correlations on quantum spaces. Int. Math. Res. Not. 2023 (2023), 12400-1–12440-41.
  5. J. Krajczok & P.M. Sołtan: The quantum disk is not a quantum group J. Top. Anal. 15 (2023), 401–411.
  6. P.M. Sołtan: Mathematics and physics of sound and music Atti dell'Accademia Polacca VIII (2020), 7–15.
  7. P. Kasprzak & P.M. Sołtan: Quantum groups with projection and extensions of locally compact quantum groups. J. Noncommut. Geom. 14 (2020), 105–123.
  8. M. Kalantar, P. Kasprzak, A. Skalski & P.M. Sołtan: Induction for locally compact quantum groups revisited. Proc. Roy. Soc. Edinburgh Sect. A 150 (2020), 1071–1093.
  9. P. Kasprzak & P.M. Sołtan: The Lattice of Idempotent States on a Locally Compact Quantum Group. Publ. Res. Inst. Math. Sci. 56 (2020), 33–53.
  10. P.M. Sołtan: Podleś Spheres for the Braided Quantum \(\operatorname{SU}(2)\). Linear Algebra Appl. 591 (2020), 169–204.
  11. P. Kasprzak, F. Khosravi & P.M. Sołtan: Kawada-Itô-Kelley Theorem for Quantum Semigroups. J. Math. Anal. Appl. 483 (2019), 123594-1–123594-15.
  12. P.M. Sołtan: Normal idempotent states on a locally compact quantum group. Mathematisches Forschungsinstitut Oberwolfach Report 22 (2018) 1364–1367.
  13. P.M. Sołtan: Quantum Semigroups from Synchronous Games. J. Math. Phys. 60 (2019) 042203-1–042203-8.
  14. J. Krajczok & P.M. Sołtan: Compact quantum groups with representations of bounded degree. J. Operator Th. 80 (2018), 415–428.
  15. K. De Commer, P. Kasprzak, A. Skalski & P.M. Sołtan: Quantum actions on discrete quantum spaces and a generalization of Clifford's theory of representations. Israel J. Math. 226 (2018), 475–503.
  16. P. Kasprzak, F. Khosravi & P.M. Sołtan: Integrable actions and quantum subgroups. Int. Math. Res. Not. 2018 (2017), 3224–3254.
  17. P. Józiak, P. Kasprzak & P.M. Sołtan: Hopf images in locally compact quantum groups. J. Math. Anal. Appl. 445 (2017), 141–166.
  18. P. Kasprzak, A. Skalski & P.M. Sołtan: The canonical central exact sequence for locally compact quantum groups. Math. Nachr. 290, No. 8–9, (2017) 1303–1316.
  19. U. Franz, A. Skalski & P.M. Sołtan: Introduction to compact and discrete quantum groups. Banach Center Publications 111 (2017), U. Franz, A. Skalski, P.M. Sołtan eds., 9–31.
  20. J. Krajczok & P.M. Sołtan: Center of the algebra of functions on the quantum group \(\mathrm{SU}_q(2)\) and related topics. Comment. Math. 56 (2016), 251–272.
  21. A. Skalski & P.M. Sołtan: Quantum families of invertible maps and related problems. Canad. J. Math. 68 (2016), 698–720.
  22. P. Kasprzak & P.M. Sołtan: Quantum groups with projection on von Neumann algebra level. J. Math. Anal. Appl. 427 (2015), 289–306.
  23. P. Kasprzak, P.M. Sołtan & S.L. Woronowicz: Quantum automorphism groups of finite quantum groups are classical. J. Geom. Phys. 89 (2015), 32–37.
  24. J. Bhowmick, A. Skalski & P.M. Sołtan: Quantum group of automorphisms of a finite (quantum) group. J. Algebra 423 (2015), 514–537.
  25. A. Skalski & P.M. Sołtan: Projective limits of quantum symmetry groups and the doubling construction for Hopf algebras. Infin. Dimens. Anal. Quantum. Probab. Relat. Top. 17 (2014), 1450012-1–1450012-27.
  26. P. Kasprzak & P.M. Sołtan: Embeddable quantum homogeneous spaces. J. Math. Anal. Appl. 411 (2014), 574–591.
  27. P.M. Sołtan & A. Viselter: A note on amenability of locally compact quantum groups. Canad. Math. Bull. 57 (2014), no. 2, 424–430.
  28. P.M. Sołtan: On quantum maps into quantum semigroups. Houston J. Math. 40, No. 3 (2014), 779–790.
  29. P.M. Sołtan: Quantum families of maps. The 15th International Workshop for Young Mathematicians "Functional Analysis", Jagiellonian University, Kraków 2013, pages 107–122.
  30. M. Daws, P. Kasprzak, A. Skalski & P.M. Sołtan: Closed quantum subgroups of locally compact quantum groups. Adv. Math. 231 (2012), 3473–3501.
  31. T. Banica, A. Skalski & P.M. Sołtan: Noncommutative homogeneous spaces: the matrix case. J. Geom. Phys. 62 (2012), 1451–1466.
  32. J. Liszka-Dalecki & P.M. Sołtan: Quantum isometry groups of symmetric groups. Int. J. Math. 23 vol. 7 (2012), 1250074-1–1250074-25.
  33. D. Kyed & P.M. Sołtan: Property (T) and exotic quantum group norms. J. Noncommut. Geom. 6 (2012), 773–800.
  34. P.M. Sołtan: On actions of compact quantum groups. Illinois J. Math. 55 no. 3 (2011), 953–962.
  35. P.M. Sołtan: Examples of non-compact quantum group actions. J. Math. Anal. Appl. 372 (2010), 224–236.
  36. P.M. Sołtan: When is a quantum space not a group?. Banach Algebras 2009, Banach Center Publications 91 (2010), R.J. Loy, V. Runde, A. Sołtysiak eds., 353–364.
  37. P.M. Sołtan: Quantum spaces without group structure. Proc. Amer. Math. Soc. 138 (2010), 2079–2086. On arXiv under the title "Non existence of group structure on some quantum spaces".
  38. P.M. Sołtan: Quantum SO(3) groups and quantum group actions on M2. J. Noncommut. Geom. 4 (2010), 2–28.
  39. P.M. Sołtan: On quantum semigroup actions on finite quantum spaces. Infin. Dimens. Anal. Quantum. Probab. Relat. Top. 12 no. 3 (2009), 503–509.
  40. P.M. Sołtan: Quantum families of maps and quantum semigroups on finite quantum spaces. J. Geom. Phys. 59 (2009) 354–368.
  41. P.M. Sołtan: Examples of quantum commutants. "Interactions of Algebraic & Coalgebraic Structures (Theory and Applications)", Arab J. Sci. Eng. 33 no. 2C (2008), 447–457.
  42. P.M. Sołtan & S.L. Woronowcz: From multiplicative unitaries to quantum groups II. J. Funct. Anal. 252 (1) (2007), 42–67.
  43. P.M. Sołtan: Compactifications of discrete quantum groups. Preprint of Westfälische Wilhelms-Universität Münster, Alg. Rep. Th. 9 no. 6 (2006), 581–591.
  44. P.M. Sołtan: Quantum Bohr compactification. Illinois J. Math. 49 (4) (2005), 1245–1270.
  45. P.M. Sołtan: New quantum "az+b" groups. Rev. Math. Phys. 17 no. 3 (2005), 313–364.
  46. W. Pusz & P.M. Sołtan: Functional form of unitary representations of the quantum "az+b" group. Rep. Math. Phys. 52 no. 2 (2003), 309–319.
  47. P.M. Sołtan & S.L. Woronowcz: A remark on manageable multiplicative unitaries. Lett. Math. Phys. 57 (2001), 239–252.
  48. P.M. Sołtan: A remark on the spectrum of the analytic generator. Rep. Math. Phys. 48 no. 3 (2001), 407–414.

Preprints

  1. A. Bochniak, I. Chełstowski, P. Kasprzak & P.M. Sołtan: Quantum Mycielskians: symmetries, twin vertices and distinguishing labelings. Preprint.
  2. J. Krajczok & P.M. Sołtan: On certain invariants of compact quantum groups. Preprint.
  3. W. Pusz & P.M. Sołtan: On some low dimensional quantum groups. Chapter in a monograph to be published by the European Mathematical Society Publishing House.
  4. W. Pusz & P.M. Sołtan: Analysis on a homogeneous space of a quantum group. Preprint.

Notes in English

  1. Quantum semigroup structures on quantum families of maps. Lecture notes from the 7th ILJU School of Mathematics "Banach Spaces and Related Topics"
  2. Groups, algebras and means.
  3. Uniqueness of the hyperfinite II_1 factor.
  4. Amenability and exactness for group actions and operator algebras.
  5. Affine isometric actions on Hilbert spaces and amenability.
  6. C*-algebras, group actions and crossed products (lecture notes).
  7. A survey of quantum "az+b" groups.

Notes in Polish

  1. Prostota \(\mathrm{C}^*_r(\mathbb{F}_2)\).
  2. Twierdzenie o imprymitywności.
  3. Teoria Tomity-Takesakiego.
  4. Twierdzenie Kreina-Smuliana.
  5. Minimalne działanie grupy SUq(N) na pełnym faktorze - notatki z pracy Y. Uedy.
  6. Geometryczna teoria grup.
  7. Reprezentacje indukowane i teoria Mackeya.

Books