Vol. 82, No. 1, 1979

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Cāˆ—-algebras associated with free products of groups

William Lindall Paschke and Norberto Salinas

Vol. 82 (1979), No. 1, 211ā€“221
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
Authors
William Lindall Paschke
Norberto Salinas