C*-norms for tensor products of discrete group C*-algebras

Matthew Wiersma

doi:10.1112/blms/bdu115

C-norms for tensor products of discrete group C-algebras

Operator Algebras 2015-06-12 v2 Functional Analysis

Authors: Matthew Wiersma

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Abstract

Let $\Gamma$ be a discrete group. We show that if $\Gamma$ is nonamenable, then the algebraic tensor products $C^*_r(\Gamma)\otimes C^*_r(\Gamma)$ and $C^*(\Gamma)\otimes C^*_r(\Gamma)$ do not admit unique $C^*$ -norms. Moreover, when $\Gamma_1$ and $\Gamma_2$ are discrete groups containing copies of noncommutative free groups, then $C^*_r(\Gamma_1)\otimes C^*_r(\Gamma_2)$ and $C^*(\Gamma_1)\otimes C_r^*(\Gamma_2)$ admit $2^{\aleph_0}$ $C^*$ -norms. Analogues of these results continue to hold when these familiar group $C^*$ -algebras are replaced by appropriate intermediate group $C^*$ -algebras.

Keywords

c*-algebras discrete groups tensor products c*-norms nonamenable groups free groups intermediate group c*-algebras

Cite

@article{arxiv.1406.2654,
  title  = {C*-norms for tensor products of discrete group C*-algebras},
  author = {Matthew Wiersma},
  journal= {arXiv preprint arXiv:1406.2654},
  year   = {2015}
}

Comments

6 pages, v2 contains minor changes and an extra remark. To appear in Bulletin of the London Mathematical Society