The full group C*-algebra of the modular group is primitive

Erik Bedos; Tron Omland

The full group C*-algebra of the modular group is primitive

Operator Algebras 2010-03-30 v2 Group Theory

Authors: Erik Bedos , Tron Omland

Abstract

We show that the full group C $^*$ -algebra of $PSL(n, \Z)$ is primitive when $n=2$ , and not primitive when $n\geq 3$ . Moreover, we show that there exists an uncountable family of pairwise inequivalent, faithful irreducible representations of $C^*(PSL(2,\Z))$ .

Keywords

group C*-algebra primitive C*-algebra modular group PSL(n,Z) irreducible representations

Cite

@article{arxiv.0906.4916,
  title  = {The full group C*-algebra of the modular group is primitive},
  author = {Erik Bedos and Tron Omland},
  journal= {arXiv preprint arXiv:0906.4916},
  year   = {2010}
}

Comments

14 pages. Some changes in the exposition.

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