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Characterization of linear groups whose reduced C*-algebras are simple

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arxiv 0812.2486 v7 pith:WYIT2XZC submitted 2008-12-12 math.GR math.OA

Tal Poznansky This is my paper · ORCID
classification math.GRmath.OA
keywords algebralinearreducedsimpleaforementionedalgebrasamenablecharacterization
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The reduced C*-algebra of a countable linear group G is shown to be simple if and only if G has no nontrivial normal amenable subgroups. Moreover, these conditions are shown to be equivalent to the uniqueness of tracial state on the aforementioned C*-algebra.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Primality and the ideal intersection property for reduced crossed products

    math.OA 2025-04 conditional novelty 8.0 of 10

    Reduced crossed products over discrete groups are prime, and the ideal intersection property holds for FC-hypercentral groups, exactly when certain conjugacy classes of elements acting 'inner' on invariant subalgebras...

  2. The geometry of triples of antipodal ideal chambers of affine buildings

    math.GR 2026-08 conditional novelty 7.0 of 10

    This paper proves that, among irreducible affine Weyl groups of rank at least two, every antipodal triple of ideal chambers is generic exactly for the types C2, G2, and B3.

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