C^∗-algebras associated with free products of groups

William Lindall Paschke and Norberto Salinas

Vol. 82 (1979), No. 1, 211–221

DOI: 10.2140/pjm.1979.82.211

Abstract

We show that the C^∗-algebra of the left regular representation of the free product of two nontrivial groups, not both of order 2, is simple and has a unique tracial state. In the case of the free product of cyclic groups, we investigate weak versus strong triviality for extensions of this C^∗-algebra. One consequence of our extension-theoretic results is that the algebras of n × n matrices (n = 1,2,⋯) over the C^∗-algebra of the left regular representation of the free product of two cyclic groups are pairwise nonisomorphic.

Mathematical Subject Classification 2000

Primary: 22D25

Secondary: 46L05

Milestones

Received: 11 September 1978

Published: 1 May 1979