Summary: Journal of Functional Analysis 243 (2007) 345351
Relatively hyperbolic groups are C-simple
, A. Minasyan
Université de Genève, Section de Mathématiques, 2-4 rue du Lièvre, Case postale 64, 1211 Genève 4, Switzerland
Received 26 May 2006; accepted 12 June 2006
Available online 14 July 2006
Communicated by D. Voiculescu
We characterize relatively hyperbolic groups whose reduced C-algebra is simple as those, which have
no non-trivial finite normal subgroups.
© 2006 Elsevier Inc. All rights reserved.
Keywords: Relatively hyperbolic groups; Reduced group C-algebras
Let G be a countable discrete group. We denote by 2(G) the Hilbert space of square-
summable complex-valued functions on G and by B( 2(G)) the algebra of bounded operators
on 2(G). The group G acts on 2(G) by means of the left regular representation:
(g)f (h) = f g-1
h , g,h G, f 2