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References
C. A. Akemann, Operator algebras associated with Fuchsian groups,Houston J. Math.,7 (1981), 295–301.
C. A. Akemann andP. A. Ostrand, Computing norms in group C*-algebras,Amer. J. Math.,98 (1976), 1015–1047.
M. Bekka, M. Cowling andP. de La Harpe, Simplicity of the reduced C*-algebra of PSL(n,Z),Inter. Math. Res. Not.,7 (1994), 285–291.
Y. Benoist andF. Labourie, Sur les difféomorphismes d’Anosov affines à feuilletages stable et instable différentiables,Invent. Math.,111 (1993), 285–308.
W. Ballmann, M. Gromov andV. Schroeder,Manifolds of Nonpositive Curvature, Birkhäuser, 1985.
D. I. Cartwright, A. M. Mantero, T. Steger andA. Zappa, Groups acting simply transitively on the vertices of a building of type Ã2, I,Geom. Ded.,47 (1993), 143–166.
D. I. Cartwright, A. M. Mantero, T. Steger andA. Zappa, Groups acting simply transitively on the vertices of a building of type Ã2, II,Geom. Ded.,47 (1993), 167–223.
J. Dixmier,Les C*-algèbres et leurs représentations, Gauthiers-Villars, 1969.
P. Eberlein andB. O’Neill, Visibility manifolds,Pacific J. Math.,46 (1973), 45–110.
I. A. Gol’dsheid andG. A. Margulis, A condition for simplicity of the spectrum of Lyapunov exponents,Soviet Math. Dokl.,35 (1987), 309–313.
Y. Guivarc’h andA. Raugi, Propriétés de contraction d’un semi-groupe de matrices inversibles,Israel J. Math.,65 (1989), 165–196.
P. de la Harpe, Reduced C*-algebras of discrete groups which are simple with unique trace,Springer Lecture Notes in Math.,1132 (1985), 230–253.
P. de la Harpe, Free subgroups in linear groups,L’Enseignement Math.,29 (1983), 129–144.
P. de la Harpe, Groupes hyperboliques, algèbres d’opérateurs, et un théorème de Jolissaint,C. R. Acad. Sci. Paris,307, Série I (1988), 771–774.
U. Haagerup andG. Pisier, Bounded linear operators between C*-algebras,Duke Math. J.,71 (1993), 889–925.
P. de la Harpe andG. Skandalis, Powers’ property and simple C*-algebras,Math. Ann.,273 (1986), 241–250.
R. E. Howe andJ. Rosenberg, The unitary representation theory of GL(n) of an infinite discrete field,Israel J. Math.,67 (1989), 67–81.
A. A. Kirillov, Positive definite functions on a group of matrices with elements from a discrete field,Soviet Math. Dokl.,6 (1965), 707–709.
M. Leinert, Faltungsoperatoren auf gewissen diskreten Gruppen,Studia Math.,52 (1974), 149–158.
G. D. Mostow,Strong Rigidity of Locally Symmetric Spaces, Princeton University Press, 1973.
W. Paschke andN. Salinas, C*-algebras associated with the free products of groups,Pacific J. Math.,82 (1979), 211–221.
R. T. Powers, Simplicity of the C*-algebra associated with the free group on two generators,Duke Math. J.,42 (1975), 151–156.
J. Rosenberg, Un complément à un théorème de Kirillov sur les caractères de GL(n) d’un corps infini discret,C. R. Acad. Sci. Paris,309, Série I (1989), 581–586.
J. Tits, Free subgroups in linear groups,J. Algebra,20 (1972), 250–270.
N. Wallach,Harmonic Analysis on Homogeneous Spaces, Marcel Dekker, 1973.
G. Warner,Harmonic Analysis on Semisimple Lie Groups I, Springer-Verlag, 1972.
R. J. Zimmer,Ergodic Theory and Semisimple Groups, Birkhäuser, 1984.
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This research was partially financed by the Australian Research Council, which supported the first two authors as Senior Research Associate at the University of New South Wales and Senior Research Fellow.
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Bekka, M., Cowling, M. & de la Harpe, P. Some groups whose reduced C*-algebra is simple. Publications Mathématiques de L’Institut des Hautes Scientifiques 80, 117–134 (1994). https://doi.org/10.1007/BF02698898
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DOI: https://doi.org/10.1007/BF02698898