Lp-representations of discrete quantum groups

References

[1] T. Banica, Théorie des représentations du groupe quantique compact libre O⁢(n), C. R. Acad. Sci. Paris Sér. I Math. 322 (1996), no. 3, 241–244. Suche in Google Scholar

[2] T. Banica, Le groupe quantique compact libre U⁢(n), Comm. Math. Phys. 190 (1997), 143–172. 10.1007/s002200050237Suche in Google Scholar

[3] E. Bédos and L. Tuset, Amenability and co-amenability for locally compact quantum groups, Internat. J. Math. 14 (2003), no. 8, 865–884. 10.1142/S0129167X03002046Suche in Google Scholar

[4] J. Bergh and J. Löfström, Interpolation spaces: An introduction, Springer, Berlin 1976. 10.1007/978-3-642-66451-9Suche in Google Scholar

[5] 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/s00220-005-1442-2Suche in Google Scholar

[6] M. Brannan, Approximation properties for free orthogonal and free unitary quantum groups, J. reine angew. Math. 672 (2012), 223–251. 10.1515/CRELLE.2011.166Suche in Google Scholar

[7] M. Brannan, M. Daws and E. Samei, Completely bounded representations of convolution algebras of locally compact quantum groups, Münster J. Math. 6 (2013), no. 2, 445–482. Suche in Google Scholar

[8] N. Brown and E. Guentner, New C∗-completions of discrete groups and related spaces, Bull. Lond. Math. Soc. 45 (2013), no. 6, 1181–1193. 10.1112/blms/bdt044Suche in Google Scholar

[9] A. Buss and R. Meyer, Square-integrable coactions of locally compact quantum groups, Rep. Math. Phys. 63 (2009), no. 2, 191–224. 10.1016/S0034-4877(09)00013-5Suche in Google Scholar

[10] M. Cowling, U. Haagerup and R. Howe, Almost L2 matrix coefficients, J. reine angew. Math. 387 (1988), 97–110. 10.1515/crll.1988.387.97Suche in Google Scholar

[11] K. Davidson, C∗-algebras by example, Fields Inst. Monogr. 6, American Mathematical Society, Providence 1996. 10.1090/fim/006Suche in Google Scholar

[12] M. Daws, Multipliers, self-induced and dual Banach algebras, Dissertationes Math. 470 (2010). 10.4064/dm470-0-1Suche in Google Scholar

[13] M. Daws, Completely positive multipliers of quantum groups, Internat. J. Math. 23 (2012), no. 12, Article ID 1250132. 10.1142/S0129167X12501327Suche in Google Scholar

[14] M. Daws, P. Fima, A. Skalski and S. White, The Haagerup property for locally compact quantum groups, J. reine angew. Math. (2014), 10.1515/crelle-2013-0113. 10.1515/crelle-2013-0113Suche in Google Scholar

[15] M. Daws, P. Kasprzak, A. Skalski and P. Soltan, Closed quantum subgroups of locally compact quantum groups, Adv. Math. 231 (2012), no. 6, 3473–3501. 10.1016/j.aim.2012.09.002Suche in Google Scholar

[16] M. Daws and P. Salmi, Completely positive definite functions and Bochner’s theorem for locally compact quantum groups, J. Funct. Anal. 264 (2013), no. 7, 1525–1546. 10.1016/j.jfa.2013.01.017Suche in Google Scholar

[17] K. De Commer, A. Freslon and M. Yamashita, CCAP for universal discrete quantum groups, Comm. Math. Phys. 331 (2014), no. 2, 677–701. 10.1007/s00220-014-2052-7Suche in Google Scholar

[18] E. G. Effros and Z.-J. Ruan, Discrete quantum groups. I: The Haar measure, Internat. J. Math. 5 (1994), no. 5, 681–723. 10.1142/S0129167X94000358Suche in Google Scholar

[19] E. G. Effros and Z.-J. Ruan, Operator spaces, London Math. Soc. Monogr. Ser. 23, Oxford University Press, New York 2000. Suche in Google Scholar

[20] P. Eymard, L’algèbre de Fourier d’un groupe localement compact, Bull. Soc. Math. France 92 (1964). 10.24033/bsmf.1607Suche in Google Scholar

[21] U. Haagerup, An example of a nonnuclear C∗-algebra, which has the metric approximation property, Invent. Math. 50 (1978/79), 279–293. 10.1007/BF01410082Suche in Google Scholar

[22] M. Kalantar, On harmonic non-commutative Lp-operators on locally compact quantum groups, Proc. Amer. Math. Soc. 141 (2013), no. 11, 3969–3976. 10.1090/S0002-9939-2013-11763-6Suche in Google Scholar

[23] S. Kaliszewski, M. B. Landstad and J. Quigg, Exotic group C∗-algebras in noncommutative duality, New York J. Math. 19 (2013), 689–711. Suche in Google Scholar

[24] J. Kustermans, Locally compact quantum groups in the universal setting, Internat. J. Math. 12 (2001), no. 3, 289–338. 10.1142/S0129167X01000757Suche in Google Scholar

[25] 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)01055-7Suche in Google Scholar

[26] J. Kustermans and S. Vaes, Locally compact quantum groups in the von Neumann algebraic setting, Math. Scand. 92 (2003), no. 1, 68–92. 10.7146/math.scand.a-14394Suche in Google Scholar

[27] D. Kyed and P. Soltan, Property (T) and exotic quantum group norms, J. Noncommut. Geom. 6 (2012), no. 4, 773–800. 10.4171/JNCG/105Suche in Google Scholar

[28] R. Okayasu, Free group C∗-algebras associated with ℓp, Internat. J. Math. 25 (2014), no. 7, Article ID 1450065. 10.1142/S0129167X14500657Suche in Google Scholar

[29] G. Pisier, Introduction to operator space theory, London Math. Soc. Lecture Note Ser. 294, Cambridge University Press, Cambridge 2003. 10.1017/CBO9781107360235Suche in Google Scholar

[30] P. Podleś and S. Woronowicz, Quantum deformation of Lorentz group, Comm. Math. Phys. 130 (1990), no. 3, 381–431. 10.1007/BF02473358Suche in Google Scholar

[31] Z.-J. Ruan, Amenability of Hopf von Neumann algebras and Kac algebras, J. Funct. Anal. 139 (1996), no. 2, 466–499. 10.1006/jfan.1996.0093Suche in Google Scholar

[32] R. Tomatsu, Amenable discrete quantum groups, J. Math. Soc. Japan 58 (2006), no. 4, 949–964. 10.2969/jmsj/1179759531Suche in Google Scholar

[33] S. Vaes, Locally compact quantum groups, Doctoral thesis, Katholieke Universiteit Leuven, 2001. Suche in Google Scholar

[34] S. Vaes and A. Van Daele, Hopf C∗-algebras, Proc. Lond. Math. Soc. (3) 82 (2001), 337–384. 10.1112/S002461150101276XSuche in Google Scholar

[35] 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/S0012-7094-07-14012-2Suche in Google Scholar

[36] A. Van Daele and S. Wang, Universal quantum groups, Internat. J. Math. 7 (1996), no. 3, 255–263. 10.1142/S0129167X96000153Suche in Google Scholar

[37] 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.2003.07.017Suche in Google Scholar

[38] R. Vergnioux, Orientation of quantum Cayley trees and applications, J. reine angew. Math. 580 (2005), 101–138. 10.1515/crll.2005.2005.580.101Suche in Google Scholar

[39] R. Vergnioux, The property of rapid decay for discrete quantum groups, J. Operator Theory 57 (2007), no. 2, 303–324. Suche in Google Scholar

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

[41] S. Woronowicz, Compact quantum groups, Symétries quantiques (Les Houches 1995), North-Holland, Amsterdam (1998), 845–884. Suche in Google Scholar