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arXiv:0812.2486 [math.GR]AbstractReferencesReviewsResources

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

Tal Poznansky

Published 2008-12-12, updated 2009-05-24Version 7

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.

Comments: 42 pages; In previous versions, statement of Proposition 2.11 was erroneous. Here is the list of resulting corrections: statement and proof of Proposition 2.11; Remark 2.12; statements of Proposition 2.17 and Theorems 6.4 and 6.5; proof of Theorem 6.3; addition of Lemma 6.6
Categories: math.GR, math.OA
Subjects: 22D25, 46L05
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