Some groups whose reduced C*-algebra is simple

Bekka, M. Bachir; Cowling, Michael; Harpe, Pierre de la

doi:10.1007/bf02698898

Cited by 51 publications

(91 citation statements)

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“…The simplicity of C * red (F n ) was proved in [16], and Powers' method has been extended to various free products [1], [13], or C * -algebras of discrete groups [5], [9], [10]. The proofs use technical estimates inside B(l 2 (A, τ )), which "move towards 0" any element having trace 0, by using sums of inner automorphisms, i.e.…”

Section: Powers' Propertymentioning

confidence: 99%

Le Groupe Quantique Compact Libre U(n)

Banica

1997

Communications in Mathematical Physics

145

334

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Abstract. The free analogues of U (n) in Woronowicz's compact quantum group theory are the quantum groups {A u (F )|F ∈ GL(n, C)} introduced by Van Daele and Wang. We classify here their irreducible representations. Their fusion rules turn to be related to the combinatorics of Voiculescu's circular variable. If FF ∈ RI n we find an embeddingis the deformation of SU (2) that we previously studied. We use the representation theory and Powers' method for showing that the reduced algebras A u (F ) red are simple, with at most one trace.

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Section: Powers' Propertymentioning

confidence: 99%

Le Groupe Quantique Compact Libre U(n)

Banica

1997

Communications in Mathematical Physics

145

334

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“…In this case one can be more precise: the action (GÂP, 1 ) is n(W)-filling. The proof follows from the remarks in [BCH,p. 127].…”

Section: Examplesmentioning

confidence: 92%

Simple Purely Infinite C*-Algebras and n-Filling Actions

Jolissaint

Robertson

2000

Journal of Functional Analysis

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Let n be a positive integer. We introduce a concept, which we call the n-filling property, for an action of a group on a separable unital C*-algebra A. If A=C(0) is a commutative unital C*-algebra and the action is induced by a group of homeomorphisms of 0 then the n-filling property reduces to a weak version of hyperbolicity. The n-filling property is used to prove that certain crossed product C*-algebras are purely infinite and simple. A variety of group actions on boundaries of symmetric spaces and buildings have the n-filling property. An explicit example is the action of 1=SL n (Z) on the projective n-space. Academic Press

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“…He proved that C; (1F) is simple (that is, has no non trivial two-sided ideals). We give below a quick proof of Powers'result, inspired by [BeCoHa94].…”

Section: Simplicity Of Reduced C*-algebrasmentioning

confidence: 94%