Simplicity of the reduced C-*-algebras of certain Coxeter groups

Details Simplicity of the reduced C-*-algebras of certain Coxeter groups Simplicity of the reduced C-*-algebras of certain Coxeter groups

2003-08-27

arxiv.org/abs/math/0308255v1

Illinois Journal of Mathematics Vol.47, No. 3 (2003)

Mathematics

Operator Algebras

15 pages, LaTeX

Scientific paper

Let (G,S) be a finitely generated Coxeter group, such that the Coxeter system is indecomposable and the canonical bilinear form is indefinite but non-degenerate. We show that the reduced C-*-algebra of G is simple with unique normalised trace. For an arbitrary finitely generated Coxeter group we prove the validity of a Haagerup inequality: There exist constants C>0 and a natural number L such that for a function f in l^2(G) supported on elements of length n with respect to the generating set S: || f * h || <= C(n+1)^{3/2 L} || f || || h ||, forall h in l^2(G).

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