We show that the full group C$^*$-algebra of the free product of two
nontrivial countable amenable discrete groups, where at least one of them has
more than two elements, is primitive. We also show that in many cases, this
C$^*$-algebra is antiliminary and has an uncountable family of pairwise
inequivalent, faithful irreducible representations.Comment: 18 pages. Preliminary version. Comments are wellcome

Bédos, Erik

Omland, Tron

English

arXiv

We show that the full group C*-algebra of the free product of two nontrivial countable amenable discrete groups, where at least one of them has more than two elements, is primitive. We also show that in many cases, this C*-algebra is antiliminary and has an uncountable family of pairwise inequivalent, faithful irreducible representations

Primitivity of some full group C $^*$ -algebras

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