Geodesic
QUANTUM INCREASING SEQUENCES GENERATE QUANTUM PERMUTATION GROUPS
Glasgow mathematical journal, Tome 62 (2020) no. 3, pp. 631-639

Voir la notice de l'article provenant de la source Cambridge University Press

We answer a question of Skalski and Sołan (2016) about inner faithfulness of the Curran’s map of extending a quantum increasing sequence to a quantum permutation. Roughly speaking, we find a inductive setting in which the inner faithfulness of Curran’s map can be boiled down to inner faithfulness of similar map for smaller algebras and then rely on inductive generation result for quantum permutation groups of Brannan, Chirvasitu and Freslon (2018). 
JÓZIAK, PAWEŁ. QUANTUM INCREASING SEQUENCES GENERATE QUANTUM PERMUTATION GROUPS. Glasgow mathematical journal, Tome 62 (2020) no. 3, pp. 631-639. doi: 10.1017/S0017089519000387
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     title = {QUANTUM {INCREASING} {SEQUENCES} {GENERATE} {QUANTUM} {PERMUTATION} {GROUPS}},
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[1] Banica, T., Truncation and duality results for Hopf image algebras, Bull. Pol. Acad. Sci. Math., 62 (2014), 161–180. Google Scholar | DOI

[2] Banica, T., Homogeneous quantum groups and their easiness level, arXiv e-prints. arXiv:1806.06368 (2018). Google Scholar

[3] Banica, T. and Bichon, J., Quantum groups acting on 4 points, J. Reine Angew. Math., 626 (2009), 75–114. Google Scholar

[4] Banica, T. and Bichon, J., Hopf images and inner faithful representations, Glasg. Math. J., 52 (2010), 677–703. Google Scholar | DOI

[5] Banica, T. and Speicher, R., Liberation of orthogonal Lie groups, Adv. Math., 222 (2009), 1461–1501. Google Scholar | DOI

[6] Bichon, J. and Yuncken, R., Quantum subgroups of the compact quantum group SU(3), Bull. Lond. Math. Soc., 46 (2014), 315–328. Google Scholar | DOI

[7] Brannan, M., Chirvasitu, A., and Freslon, A., Topological generation and matrix models for quantum reflection groups, arXiv e-prints, arXiv:1808.08611 (2018). Google Scholar

[8] Brannan, M., Collins, B., and Vergnioux, R., The Connes embedding property for quantum group von Neumann algebras, Trans. Amer. Math. Soc., 369 (2017), 3799–3819. Google Scholar | DOI

[9] Chirvasitu, A., Residually finite quantum group algebras, J. Funct. Anal., 268 (2015), 3508–3533. Google Scholar | DOI

[10] Curran, S., A characterization of freeness by invariance under quantum spreading, J. Reine Angew. Math., 659 (2011), 43–65. Google Scholar

[11] Daws, M., Kasprzak, P., Skalski, A., and Sołtan, P. M., Closed quantum subgroups of locally compact quantum groups, Adv. Math., 231 (2012), 3473–3501. Google Scholar | DOI

[12] Józiak, P., Hopf images in Locally Compact Quantum Groups, PhD Thesis (IMPAN, 2017). Google Scholar | DOI

[13] Józiak, P., Remarks on Hopf images and quantum permutation groups , Canad. Math. Bull., 61 (2018), 301–317. Google Scholar | DOI

[14] Józiak, P., Kasprzak, P., and Sołtan, P. M., Hopf images in locally compact quantum groups, J. Math. Anal. Appl., 455 (2017), 141–166. Google Scholar | DOI

[15] Köstler, C. and Speicher, R., A noncommutative de Finetti theorem: Invariance under quantum permutations is equivalent to freeness with amalgamation, Comm. Math. Phys., 291 (2009), 473–490. Google Scholar | DOI

[16] Kyed, D. and Sołtan, P. M., Property (T) and exotic quantum group norms, J. Noncommut. Geom., 6 (2012), 773–800. Google Scholar | DOI

[17] Neshveyev, S. and Tuset, L., Compact quantum groups and their representation categories, vol. 20. Cours Spécialisés [Specialized Courses] (Société Mathématique de France, Paris, 2013). Google Scholar

[18] Podleś, P., Symmetries of quantum spaces. Subgroups and quotient spaces of quantum and groups, Comm. Math. Phys., 170 (1995), 1–20. Google Scholar | DOI

[19] Skalski, A. and Sołtan, P. M., Quantum families of invertible maps and related problems, Canad. J. Math., 68 (2016), 698–720. Google Scholar | DOI

[20] Timmermann, T., An Invitation to Quantum Groups and Duality (EMS Textbooks in Mathematics, European Mathematical Society (EMS), Zürich, 2008). From Hopf algebras to multiplicative unitaries and beyond. Google Scholar | DOI

[21] Wang, S., Quantum symmetry groups of finite spaces, Comm. Math. Phys., 195 (1998), 195–211. Google Scholar | DOI

[22] Woronowicz, S. L., Compact quantum groups, in Symétries quantiques (Houches, L., Editor) (North-Holland, Amsterdam, 1998), 845–884. Google Scholar

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