On the structure of quantum automorphism groups

References

[1] S. Baaj and G. Skandalis, Unitaires multiplicatifs et dualité pour les produits croisés de C*-algèbres, Ann. Sci. Éc. Norm. Supér. (4) 26 (1993), no. 4, 425–488. 10.24033/asens.1677Search in Google Scholar

[2] T. Banica, Fusion rules for representations of compact quantum groups, Expo. Math. 17 (1999), no. 4, 313–337. Search in Google Scholar

[3] T. Banica, Symmetries of a generic coaction, Math. Ann. 314 (1999), no. 4, 763–780. 10.1007/s002080050315Search in Google Scholar

[4] T. Banica, Quantum groups and Fuss–Catalan algebras, Comm. Math. Phys. 226 (2002), no. 1, 221–232. 10.1007/s002200200613Search in Google Scholar

[5] T. Banica, Quantum automorphism groups of small metric spaces, Pacific J. Math. 219 (2005), no. 1, 27–51. 10.2140/pjm.2005.219.27Search in Google Scholar

[6] T. Banica and J. Bichon, Quantum groups acting on 4 points, J. reine angew. Math. 626 (2009), 75–114. 10.1515/CRELLE.2009.003Search in Google Scholar

[7] T. Banica, J. Bichon and B. Collins, Quantum permutation groups: A survey, Noncommutative harmonic analysis with applications to probability, Banach Center Publ. 78, Institute of Mathematics of the Polish Academy of Sciences, Warsaw (2007), 13–34. 10.4064/bc78-0-1Search in Google Scholar

[8] R. Banica, S. Curran and R. Speicher, De Finetti theorems for easy quantum groups, Ann. Probab. 40 (2012), no. 1, 401–435. 10.1214/10-AOP619Search in Google Scholar

[9] T. Banica and R. Speicher, Liberation of orthogonal Lie groups, Adv. Math. 222 (2009), no. 4, 1461–1501. 10.1016/j.aim.2009.06.009Search in Google Scholar

[10] J. Bichon, A. De Rijdt and S. Vaes, Ergodic coactions with large multiplicity and monoidal equivalence of quantum groups, Comm. Math. Phys. 262 (2006), no. 3, 703–728. 10.1007/s00220-005-1442-2Search in Google Scholar

[11] M. Brannan, Reduced operator algebras of trace-perserving quantum automorphism groups, Doc. Math. 18 (2013), 1349–1402. 10.4171/dm/430Search in Google Scholar

[12] K. De Commer, Galois objects for algebraic quantum groups, J. Algebra 321 (2009), no. 6, 1746–1785. 10.1016/j.jalgebra.2008.11.039Search in Google Scholar

[13] A. De Rijdt and N. Vander Vennet, Actions of monoidally equivalent compact quantum groups and applications to probabilistic boundaries, Ann. Inst. Fourier (Grenoble) 60 (2010), no. 1, 169–216. 10.5802/aif.2520Search in Google Scholar

[14] J. H. Hong and W. Szymański, Quantum spheres and projective spaces as graph algebras, Comm. Math. Phys. 232 (2002), no. 1, 157–188. 10.1007/s00220-002-0732-1Search in Google Scholar

[15] J. Kustermans and S. Vaes, Locally compact quantum groups, Ann. Sci. Éc. Norm. Supér. (4) 33 (2000), no. 6, 837–934. 10.1016/S0012-9593(00)01055-7Search in Google Scholar

[16] R. Meyer, Homological algebra in bivariant K-theory and other triangulated categories. II, Tbil. Math. J. 1 (2008), 165–210. 10.32513/tbilisi/1528768828Search in Google Scholar

[17] R. Meyer and R. Nest, The Baum–Connes conjecture via localisation of categories, Topology 45 (2006), no. 2, 209–259. 10.1016/j.top.2005.07.001Search in Google Scholar

[18] R. Meyer and R. Nest, An analogue of the Baum–Connes isomorphism for coactions of compact groups, Math. Scand. 100 (2007), no. 2, 301–316. 10.7146/math.scand.a-15025Search in Google Scholar

[19] R. Meyer and R. Nest, Homological algebra in bivariant K-theory and other triangulated categories. I, Triangulated categories, London Math. Soc. Lecture Note Ser. 375, Cambridge University Press, Cambridge (2010), 236–289. 10.1017/CBO9781139107075.006Search in Google Scholar

[20] C. Mrozinski, Quantum automorphism groups and SO⁢(3)-deformations, J. Pure Appl. Algebra 219 (2015), no. 1, 1–32. 10.1016/j.jpaa.2014.04.006Search in Google Scholar

[21] R. Nest and C. Voigt, Equivariant Poincaré duality for quantum group actions, J. Funct. Anal. 258 (2010), no. 5, 1466–1503. 10.1016/j.jfa.2009.10.015Search in Google Scholar

[22] P. Podleś, Quantum spheres, Lett. Math. Phys. 14 (1987), no. 3, 193–202. 10.1007/BF00416848Search in Google Scholar

[23] P. M. Sołtan, Quantum SO⁢(3) groups and quantum group actions on M2, J. Noncommut. Geom. 4 (2010), no. 1, 1–28. 10.4171/JNCG/48Search in Google Scholar

[24] S. Vaes and R. Vergnioux, The boundary of universal discrete quantum groups, exactness, and factoriality, Duke Math. J. 140 (2007), no. 1, 35–84. 10.1215/S0012-7094-07-14012-2Search in Google Scholar

[25] A. Van Daele, An algebraic framework for group duality, Adv. Math. 140 (1998), no. 2, 323–366. 10.1006/aima.1998.1775Search in Google Scholar

[26] R. Vergnioux, K-amenability for amalgamated free products of amenable discrete quantum groups, J. Funct. Anal. 212 (2004), no. 1, 206–221. 10.1016/j.jfa.2003.07.017Search in Google Scholar

[27] R. Vergnioux and C. Voigt, The K-theory of free quantum groups, Math. Ann. 357 (2013), no. 1, 355–400. 10.1007/s00208-013-0902-9Search in Google Scholar

[28] C. Voigt, The Baum–Connes conjecture for free orthogonal quantum groups, Adv. Math. 227 (2011), no. 5, 1873–1913. 10.1016/j.aim.2011.04.008Search in Google Scholar

[29] C. Voigt, Quantum SU⁢(2) and the Baum–Connes conjecture, Operator algebras and quantum groups, Banach Center Publ. 98, Institute of Mathematics of the Polish Academy of Sciences, Warsaw (2012), 417–432. 10.4064/bc98-0-17Search in Google Scholar

[30] S. Wang, Quantum symmetry groups of finite spaces, Comm. Math. Phys. 195 (1998), no. 1, 195–211. 10.1007/s002200050385Search in Google Scholar