Banach Journal of Mathematical Analysis

Primitivity of some full group C*-algebras

Erik Bedos and Tron A. Omland

Full-text: Open access

Abstract

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.

Article information

Source
Banach J. Math. Anal., Volume 5, Number 2 (2011), 44-58.

Dates
First available in Project Euclid: 14 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1313363001

Digital Object Identifier
doi:10.15352/bjma/1313363001

Mathematical Reviews number (MathSciNet)
MR2780868

Zentralblatt MATH identifier
1228.46051

Subjects
Primary: 46L05: General theory of $C^*$-algebras
Secondary: 22D25: $C^*$-algebras and $W^*$-algebras in relation to group representations [See also 46Lxx] 46L55: Noncommutative dynamical systems [See also 28Dxx, 37Kxx, 37Lxx, 54H20]

Keywords
full group C*-algebra primitivity free product antiliminary

Citation

Bedos, Erik; Omland, Tron A. Primitivity of some full group C*-algebras. Banach J. Math. Anal. 5 (2011), no. 2, 44--58. doi:10.15352/bjma/1313363001. https://projecteuclid.org/euclid.bjma/1313363001


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References

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