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

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

2010-03-29

arxiv.org/abs/1003.5496v1

Mathematics

Operator Algebras

18 pages. Preliminary version. Comments are wellcome.

Scientific paper

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.

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