Primitivity of some full group [C.sup.]-algebras

Primitivity of some full group [C.sup.]-algebras

We show that the full group [C.sup.*]-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.sup.*] algebra is antiliminary and has an uncountable family of pairwi...

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Veröffentlicht in:Banach journal of mathematical analysis 2011-07, Vol.5 (2), p.44
Hauptverfasser: Bedos, Erik, Omland, Tron A
Format: Artikel
Sprache:eng
Schlagworte:
Group theory
Mathematical analysis
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Zusammenfassung:We show that the full group [C.sup.*]-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.sup.*] algebra is antiliminary and has an uncountable family of pairwise inequivalent, faithful irreducible representations. Key words and phrases. full group [C.sup.*]-algebra, primitivity, free product, antiliminary.
ISSN:1735-8787