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Geometric, probabilistic and analytic theory of topological quantum groups and its interaction with operator algebras

2014/14/E/ST1/00525

Keywords

Descriptors

  • ST1_9: Algebry operatorowe i analiza funkcjonalna

Panel

ST1 – Mathematics: all areas of mathematics, pure and applied, as well as mathematical foundations of computer science, physics and statistics

Host institution

Instytut Matematyczny Polskiej Akademii Nauk

Voivodeship: mazowieckie

Other projects carried out by the institution »

Principal investigator (from the host institution)

dr hab. Adam Grzegorz Skalski

Number of co-investigators in the project: 6

Call

SONATA BIS 4 – announced on 2014-06-16

Amount awarded
660 140 PLN
Project start date
2015-04-27
Project end date
2022-04-26
Project duration
84 months (the same as in the proposal)
Project status
Project settled

Equipment purchased [PL]

  1. Drukarka ze skanerem. Cost: 2 000 PLN
  2. Komputer przenośny (2 pcs). Cost: 14 000 PLN
  3. Komputer stacjonarny (2 pcs). Cost: 10 000 PLN
  4. monitor.

Information in the final report

Publication in academic press/journals (42)

  1. L_p-improving convolution operators on finite quantum groups

    Authors:
    Simeng Wang
    Academic press:
    Indiana University Mathematics Journal (year: 2016, volume: 65, pages: 1609-1637), Publisher: INDIANA UNIV MATH JOURNAL
    Status:
    Published
    DOI:
    10.1512/iumj.2016.65.5881 – link to the publication

  2. Nica-Toeplitz algebras associated with right tensor C∗-precategories over right LCM semigroups

    Authors:
    Bartosz Kwaśniewski, Nadia Larsen
    Academic press:
    International Journal of Mathematics (year: 2019, volume: 30, pages: 1950013), Publisher: World Scientific
    Status:
    Published
    DOI:
    10.1142/S0129167X19500137 – link to the publication

  3. The canonical central exact sequence for locally compact quantum groups

    Authors:
    Paweł Kasprzak, Adam Skalski, Piotr Sołtan
    Academic press:
    Mathematische Nachrichten (year: 2017, volume: 290, pages: 1303-1316), Publisher: Wiley
    Status:
    Published
    DOI:
    10.1002/mana.201600208 – link to the publication

  4. Integration over the quantum diagonal subgroup and associated Fourier-like algebras

    Authors:
    Uwe Franz, Hun Hee Lee, Adam Skalski
    Academic press:
    International Journal of Mathematics (year: 2016, volume: 27 (9), pages: 1650073), Publisher: World Scientific
    Status:
    Published
    DOI:
    10.1142/S0129167X16500737 – link to the publication

  5. Wreath products of finite groups by quantum groups

    Authors:
    Amaury Freslon, Adam Skalski
    Academic press:
    Journal of the Noncommutative Geometry (year: 2018, volume: 12, pages: 29-68), Publisher: European Mathematical Society
    Status:
    Published
    DOI:
    10.4171/JNCG/270 – link to the publication

  6. Classifying right-angled Hecke C*-algebras via K-theoretic invariants

    Authors:
    Sven Raum and Adam Skalski
    Academic press:
    Advances in Mathematics (year: 2022, volume: 407, pages: Paper No. 108559.), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.aim.2022.108559 – link to the publication

  7. Lévy-Khintchine decompositions for generating functionals on algebras associated to universal compact quantum groups

    Authors:
    Biswarup Das, Uwe Franz, Anna Kula, Adam Skalski
    Academic press:
    Infinite Dimensional Analysis, Quantum Probability and Related Topics (year: 2018, volume: 21, pages: 1850017, 36 pp), Publisher: World Scientific
    Status:
    Published
    DOI:
    10.1142/S0219025718500170 – link to the publication

  8. Positive Herz-Schur multipliers and approximation properties of crossed products

    Authors:
    Andrew McKee, Adam Skalski, Ivan Todorov, Lyudmila Turowska
    Academic press:
    Mathematical Proceedings of the Cambridge Philosophical Society (year: 2018, volume: 165, pages: 511–532), Publisher: Cambridge University Press
    Status:
    Published
    DOI:
    10.1017/S0305004117000639 – link to the publication

  9. Nica–Toeplitz algebras associated with product systems over right LCM semigroups

    Authors:
    Nadia Larsen i Bartosz Kwaśniewski
    Academic press:
    Journal of Mathematical Analysis and Applications (year: 2019, volume: 470, pages: Pages 532-570), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jmaa.2018.10.020 – link to the publication

  10. Open quantum subgroups of locally compact quantum groups

    Authors:
    Mehrdad Kalantar, Paweł Kasprzak, Adam Skalski
    Academic press:
    Advances in Mathematics (year: 2016, volume: 303 (3), pages: 322-359), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.aim.2016.08.010 – link to the publication

  11. Aperiodicity, topological freeness and more: from group actions to Fell bundles

    Authors:
    Bartosz Kwaśniewski, Ralf Meyer
    Academic press:
    Studia Mathematica (year: 2018, volume: 241, pages: 257-302), Publisher: Instytut Matematyczny PAN
    Status:
    Published
    DOI:
    10.4064/sm8762-5-2017 – link to the publication

  12. Noncommutative Furstenberg boundary

    Authors:
    Mehrdad Kalantar, Paweł Kasprzak, Adam Skalski i Roland Vergnioux
    Academic press:
    Analysis & PDE (year: 2022, volume: 15, pages: 795–842), Publisher: MSP (Mathematical Sciences Publishers)
    Status:
    Published
    DOI:
    10.2140/apde.2022.15.795 – link to the publication

  13. The Haagerup property for twisted groupoid dynamical systems

    Authors:
    Bartosz Kwaśniewski, Kang Li i Adam Skalski
    Academic press:
    Journal of Functional Analysis (year: 2022, volume: 283, pages: 109484, 23 pp), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jfa.2022.109484 – link to the publication

  14. Amalgamated direct sums of operator spaces

    Authors:
    Mateusz Wasilewski
    Academic press:
    Bulletin of the London Mathematical Society (year: 2016, volume: 48, pages: 155-162), Publisher: Wiley
    Status:
    Published
    DOI:
    10.1112/blms/bdv093 – link to the publication

  15. Lacunary Fourier Series for Compact Quantum Groups

    Authors:
    Simeng Wang
    Academic press:
    Communications in Mathematical Physics (year: 2017, volume: 341 (3), pages: 895–945), Publisher: Springer Verlag
    Status:
    Published
    DOI:
    10.1007/s00220-016-2670-3 – link to the publication

  16. Remarks on factoriality and $q$-deformations

    Authors:
    Adam Skalski, Simeng Wang
    Academic press:
    Proceedings of the American Mathematical Society (year: 2018, volume: 146, pages: 3813-3823), Publisher: American Mathematical Society
    Status:
    Published
    DOI:
    10.1090/proc/13715 – link to the publication

  17. The RFD and KAC quotients of the Hopf*-algebras of universal orthogonal quantum groups

    Authors:
    Biswarup Das, Uwe Franz i Adam Skalski
    Academic press:
    Annales Mathematiques Blaise Pascal (year: 2021, volume: 28, pages: 141-155), Publisher: Laboratoire de Mathématiques Blaise Pascal
    Status:
    Published
    DOI:
    10.5802/ambp.402 – link to the publication

  18. $q$-Araki-Woods algebras: Extension of second quantisation and Haagerup apparoximation property

    Authors:
    Mateusz Wasilewski
    Academic press:
    Proceedings of the American Mathematical Society (year: 2017, volume: 145, pages: 5287–5298), Publisher: American Mathematical Society
    Status:
    Published
    DOI:
    10.1090/proc/13681 – link to the publication

  19. On MASAs in q-deformed von Neumann algebras

    Authors:
    Martijn Caspers, Adam Skalski i Mateusz Wasilewski
    Academic press:
    Pacific Journal of Mathematics (year: 2019, volume: 302, pages: 46043), Publisher: MSP
    Status:
    Published
    DOI:
    10.2140/pjm.2019.302.1 – link to the publication

  20. On C*-completions of discrete quantum group rings

    Authors:
    Martijn Caspers and Adam Skalski
    Academic press:
    Bulletin of the London Mathematical Society (year: 2019, volume: 51, pages: 691-704), Publisher: Wiley
    Status:
    Published
    DOI:
    10.1112/blms.12267 – link to the publication

  21. Quantum symmetries of the twisted tensor products of C*-algebras

    Authors:
    Jyotishman Bhowmick, Arnab Mandal, Sutanu Roy and Adam Skalski
    Academic press:
    Communications in Mathematical Physics (year: 2019, volume: 368, pages: 1051-1085), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s00220-018-3279-5 – link to the publication

  22. Infinitely divisible states on finite quantum groups

    Authors:
    Haonan Zhang
    Academic press:
    Mathematische Zeitschrift (year: 2020, volume: 294, pages: 571-592), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s00209-019-02288-8 – link to the publication

  23. Nuclear dimension of simple stably projectionless C∗-algebras

    Authors:
    Jorge Castillejos, Samuel Evington
    Academic press:
    Analysis & PDE (year: 2020, volume: 13, pages: 2205-2240), Publisher: Mathematical Science Publishers
    Status:
    Published
    DOI:
    10.2140/apde.2020.13.2205 – link to the publication

  24. Induction for locally compact quantum groups revisited

    Authors:
    Mehrdad Kalantar, Paweł Kasprzak, Adam Skalski, Piotr Sołtan
    Academic press:
    Proc. Roy. Soc. Edinburgh Sect. A (year: 2020, volume: 150, pages: 1071-1093), Publisher: Cambridge University Press
    Status:
    Published
    DOI:
    10.1017/prm.2018.94 – link to the publication

  25. Nuclear dimension of simple C*-algebras

    Authors:
    Jorge Castillejos, Sam Evington, Aron Tikuisis, Stuart White and Wilhelm Winter
    Academic press:
    Inventiones Mathematicae (year: 2021, volume: 224, pages: 245-290), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s00222-020-01013-1 – link to the publication

  26. Actions of locally compact (quantum) groups on ternary rings of operators, their crossed products, and generalized Poisson boundaries

    Authors:
    Pekka Salmi, Adam Skalski
    Academic press:
    Kyoto Journal of Mathematics (year: 2017, volume: 57, pages: 667-691), Publisher: Duke University Press
    Status:
    Published
    DOI:
    10.1215/21562261-2017-0011 – link to the publication

  27. Idempotent states on Sekine quantum groups

    Authors:
    Haonan Zhang
    Academic press:
    Communications in Algebra (year: 2019, volume: 47, pages: 4095-4113), Publisher: TAYLOR & FRANCIS
    Status:
    Published
    DOI:
    10.1080/00927872.2019.1579335 – link to the publication

  28. Type I locally compact quantum groups: integral characters and coamenability

    Authors:
    Jacek Krajczok
    Academic press:
    Dissertationes Mathematicae (year: 2021, volume: 561, pages: 1-151), Publisher: IMPAN
    Status:
    Published
    DOI:
    10.4064/dm818-9-2020 – link to the publication

  29. Convolution semigroups on locally compact quantum groups and noncommutative Dirichlet forms

    Authors:
    Adam Skalski i Ami Viselter
    Academic press:
    Journal de Mathématiques Pures et Appliquées (year: 2019, volume: 124, pages: 59-105), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.matpur.2018.04.007 – link to the publication

  30. Introduction to compact and discrete quantum groups

    Authors:
    Uwe Franz, Adam Skalski, Piotr Sołtan
    Academic press:
    Banach Center Publications (year: 2017, volume: 111, pages: 11567), Publisher: Mathematical Institute, Polish Academy of Sciences
    Status:
    Published
    DOI:
    10.4064/bc111-0-1 – link to the publication

  31. From Wigner-Yanase-Dyson conjecture to Carlen-Frank-Lieb conjecture

    Authors:
    Haonan Zhang
    Academic press:
    Advances in Mathematics (year: 2020, volume: 365, pages: 107053), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.aim.2020.107053 – link to the publication

  32. Quantum actions on discrete quantum spaces and a generalization of Clifford's theory of representations.

    Authors:
    Kenny De Commer, Paweł Kasprzak, Adam Skalski and Piotr M. Sołtan
    Academic press:
    Israel Journal of Mathematics (year: 2018, volume: 226, pages: 475-503), Publisher: HEBREW UNIV MAGNES PRESS
    Status:
    Published
    DOI:
    10.1007/s11856-018-1709-x – link to the publication

  33. Maximal subgroups and von Neumann subalgebras with the Haagerup property

    Authors:
    Yongle Jiang i Adam Skalski
    Academic press:
    Groups, Geometry and Dynamics (year: 2021, volume: 15, pages: 849-892), Publisher: European Mathematical Society
    Status:
    Published
    DOI:
    10.4171/GGD/614 – link to the publication

  34. Fixed points and limits of convolution powers of contractive quantum measures

    Authors:
    Matthew Neufang, Pekka Salmi, Adam Skalski, Nico Spronk
    Academic press:
    Indiana University Mathematics Journal (year: 2021, volume: 70, pages: 1971-2009), Publisher: University of Indiana
    Status:
    Published
    DOI:
    10.1512/iumj.2021.70.8692 – link to the publication

  35. Quantum families of invertible maps and related problems

    Authors:
    Adam Skalski, Piotr Sołtan
    Academic press:
    Canadian Journal of Mathematics (year: 2016, volume: 68, pages: 698–720), Publisher: Canadian Journal of Mathematics
    Status:
    Published
    DOI:
    10.4153/CJM-2015-037-9 – link to the publication

  36. Idempotent states on locally compact quantum groups II

    Authors:
    Pekka Salmi, Adam Skalski
    Academic press:
    Quarterly Journal of Mathematocs (year: 2017, volume: 68, pages: 421–431), Publisher: Oxford University Press
    Status:
    Published
    DOI:
    10.1093/qmath/haw045 – link to the publication

  37. Around property (T) for quantum groups.

    Authors:
    Matthew Daws, Adam Skalski, Ami Viselter
    Academic press:
    Communications in Mathematical Physics (year: 2017, volume: 353, pages: 69-118), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s00220-017-2862-5 – link to the publication

  38. Maximal Haagerup subalgebras in L(Z2⋊SL2(Z))

    Authors:
    Yongle Jiang
    Academic press:
    Journal of Operator Theory (year: 2021, volume: 86, pages: 203-230), Publisher: Theta Foundation
    Status:
    Published
    DOI:
    10.7900/jot.2020mar09.2282 – link to the publication

  39. Generating Functionals for Locally Compact Quantum Groups

    Authors:
    Adam Skalski i Ami Viselter
    Academic press:
    International Mathematics Research Notices (year: 2021, volume: 14, pages: 10981-11009), Publisher: Oxford University Press
    Status:
    Published
    DOI:
    10.1093/imrn/rnz387 – link to the publication

  40. On the Baum-Connes conjecture for discrete quantum groups with torsion and the quantum Rosenberg conjecture

    Authors:
    Yuki Arano i Adam Skalski
    Academic press:
    Proceedings of the AMS (year: 2021, volume: 149, pages: 5237-5254), Publisher: American Mathematical Society
    Status:
    Published
    DOI:
    10.1090/proc/15598 – link to the publication

  41. Maximal von Neumann subalgebras arising from maximal subgroups

    Authors:
    Yongle Jiang
    Academic press:
    Science China Mathematics (year: 2021, volume: 64, pages: 2295-2312), Publisher: Springer
    Status:
    Published
    DOI:
    10.1007/s11425-020-1671-9 – link to the publication

  42. Second cohomology groups of the Hopf∗-algebras associated to universal unitary quantum groups

    Authors:
    Biswarup Das, Uwe Franz, Anna Kula i Adam Skalski
    Status:
    Accepted for publication

Articles in post-conference publications (2)

  1. Singular subgroups in A~2-groups and their von Neumann algebras

    Authors:
    Piotr Nowak and Yongle Jiang
    Conference:
    International Workshop on Operator Theory and its Applications 2018 (year: 2020, pages: 391-402), Publisher: Springer
    Date:
    conference 2018
    Status:
    Published

  2. Quantum Dirichlet forms and their recent applications

    Authors:
    Adam Skalski
    Conference:
    Geometric Methods in Physics XXXVII (year: 2018, pages: 246-254), Publisher: Birkhauser
    Date:
    conference June
    Status:
    Published

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