C*-simplicity of locally compact Powers groups

References

[1] S. Adams and W. Ballmann, Amenable isometry groups of Hadamard spaces, Math. Ann. 312 (1998), no. 1, 183–195. 10.1007/s002080050218Suche in Google Scholar

[2] M. Bekka, M. Cowling and P. de la Harpe, Simplicity of the reduced C*-algebra of PSL⁢(n,ℤ), Int. Math. Res. Not. IMRN 1994 (1994), no. 7, 285–291. 10.1155/S1073792894000322Suche in Google Scholar

[3] B. Bekka, P. de la Harpe and A. Valette, Kazhdan’s property (T), New Math. Monogr. 11, Cambridge University Press, Cambridge 2008. 10.1017/CBO9780511542749Suche in Google Scholar

[4] J. Bernstein, All reductive p-adic groups are of type I, Funct. Anal. Appl. 8 (1974), 91–93. 10.1007/BF01078592Suche in Google Scholar

[5] E. Breuillard, M. Kalantar, M. Kennedy and N. Ozawa, C*-simplicity and the unique trace property for discrete groups, preprint (2014), http://arxiv.org/abs/1410.2518. Suche in Google Scholar

[6] A. Connes, Une classification des facteurs de type III, Ann. Sci. Éc. Norm. Supér. (4) 6 (1973), 133–252. 10.24033/asens.1247Suche in Google Scholar

[7] A. Connes, Classification des facteurs, Operator algebras and applications (Kingston 1980), Proc. Sympos. Pure Math. 38. Part 2, American Mathematical Society, Providence (1982), 43–109. 10.1090/pspum/038.2/679497Suche in Google Scholar

[8] P. de la Harpe, Reduced C*-algebras of discrete groups which are simple with a unique trace, Operator algebras and their connections with topology and ergodic theory (Buşteni 1983), Lecture Notes in Math. 1132, Springer, Berlin (1985), 230–253. 10.1007/BFb0074887Suche in Google Scholar

[9] P. de la Harpe, On simplcity of reduced C*-algebras of groups, Bull. Lond. Math. Soc. 39 (2007), 1–26. 10.1112/blms/bdl014Suche in Google Scholar

[10] P. de la Harpe and J.-P. Préaux, C*-simple groups: Amalgamated free products, HNN extensions, and fundamental groups of 3-manifolds, J. Topol. Anal. 3 (2011), no. 4, 451–489. 10.1142/S1793525311000659Suche in Google Scholar

[11] J. Dixmier, C*-algebras, North-Holland, Amsterdam 1977. Suche in Google Scholar

[12] J. M. Fell, The dual spaces of C*-algebras, Trans. Amer. Math. Soc. 94 (1960), no. 3, 365–403. 10.1090/S0002-9947-1960-0146681-0Suche in Google Scholar

[13] A. Figà-Talamanca and C. Nebbia, Harmonic analysis and representation theory for groups acting on homogeneous trees, London Math. Soc. Lecture Note Ser. 162, Cambridge University Press, Cambridge 1991. 10.1017/CBO9780511662324Suche in Google Scholar

[14] J. Glimm, Type IC*-algebras, Ann. of Math. (2) 73 (1961), 572–612. 10.2307/1970319Suche in Google Scholar

[15] U. Haagerup, A new look at C*-simplicity and the unique trace property of a group, preprint (2015), http://arxiv.org/abs/1509.05880. Suche in Google Scholar

[16] Harish-Chandra, Discrete series for semisimple Lie groups. II. Explicit determination of the characters, Acta Math. 116 (1966), 1–111. 10.1007/BF02392813Suche in Google Scholar

[17] A. Ioana, S. Popa and S. Vaes, A class of superrigid group von Neumann algebras, Ann. of Math. (2) 178 (2013), 231–286. 10.4007/annals.2013.178.1.4Suche in Google Scholar

[18] I. Kaplansky, The structure of certain operator algebras, Trans. Amer. Math. Soc. 70 (1951), 219–255. 10.1090/S0002-9947-1951-0042066-0Suche in Google Scholar

[19] M. Kennedy, Characterizations of C*-simplicity, preprint (2015), http://arxiv.org/abs/1509.01870. Suche in Google Scholar

[20] J. Kustermans, KMS-weights on C*-algebras, preprint (1997), https://arxiv.org/abs/funct-an/9704008. Suche in Google Scholar

[21] J. Kustermans and S. Vaes, Weight theory for C*-algebraic quantum groups, preprint (1999), http://arxiv.org/abs/math/9901063. Suche in Google Scholar

[22] A. Le Boudec, C*-simplicity and the amenable radical, preprint (2015), http://arxiv.org/abs/1507.03452. Suche in Google Scholar

[23] W. Lück, L2-invariants and their applications to geometry, group theory and spectral theory, Ergeb. Math. Grenzgeb. (3) 44, Springer, Berlin 2001. 10.1007/978-3-642-56478-9_42Suche in Google Scholar

[24] G. W. Mackey, Induced representations of locally compact groups I, Ann. of Math. (2) 55 (1952), no. 1, 101–139. 10.2307/1969423Suche in Google Scholar

[25] D. McDuff, Uncountably many II1 factors, Ann. of Math. (2) 90 (1969), 372–377. 10.2307/1970730Suche in Google Scholar

[26] S. Murakami, On the automorphisms of a real semi-simple Lie algebra, J. Math. Soc. Japan 4 (1952), no. 2, 103–133. 10.2969/jmsj/00420103Suche in Google Scholar

[27] R. T. Powers, Simplicity of the C*-algebra associated with the free group on two generators, Duke Math. J. 42 (1975), 151–156. 10.1215/S0012-7094-75-04213-1Suche in Google Scholar

[28] J. Rosenberg, C*-algebras and Mackey’s theory of group representations, C*-algebras: 1943-1993 (San Antonio 1993), Contemp.Math. 167, American Mathematical Society, Providence (1994), 151–181. 10.1090/conm/167/1292014Suche in Google Scholar

[29] M. Takesaki, Theory of operator algebras II, Springer, Berlin 2003. 10.1007/978-3-662-10451-4Suche in Google Scholar

[30] K. Tzanev, Hecke C*-algebras and amenability, J. Operator Theory 50 (2003), no. 1, 169–178. Suche in Google Scholar

[31] D. van Dantzig, Zur topologischen Algebra. III. Brouwersche und Cantorsche Gruppen, Compos. Math. 3 (1936), 408–426. Suche in Google Scholar