Illinois Journal of Mathematics

Constructions of exotic group $C$∗-algebras

Matthew Wiersma

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Let $\Gamma$ be a discrete group. When $\Gamma$ is nonamenable, the reduced and full group $C$∗-algebras differ and it is generally believed that there should be many intermediate $C$∗-algebras, however few examples are known. In this paper, we give new constructions and compare existing constructions of intermediate group $C$∗-algebras for both generic and specific groups $\Gamma$.

Article information

Illinois J. Math., Volume 60, Number 3-4 (2016), 655-667.

Received: 3 February 2015
Revised: 19 April 2017
First available in Project Euclid: 22 September 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 22D25: $C^*$-algebras and $W^*$-algebras in relation to group representations [See also 46Lxx] 22D10: Unitary representations of locally compact groups
Secondary: 43A35: Positive definite functions on groups, semigroups, etc. 46L05: General theory of $C^*$-algebras


Wiersma, Matthew. Constructions of exotic group $C$∗-algebras. Illinois J. Math. 60 (2016), no. 3-4, 655--667. doi:10.1215/ijm/1506067285.

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