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

Bédos, Erik; Omland, Tron

doi:10.1090/S0002-9939-2011-11143-2

The full group C$^*$-algebra of the modular group is primitive
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by Erik Bédos and Tron Å. Omland

Proc. Amer. Math. Soc. 140 (2012), 1403-1411

DOI: https://doi.org/10.1090/S0002-9939-2011-11143-2

Published electronically: August 10, 2011

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Abstract:

We show that the full group C$^*$-algebra of $PSL(n, \mathbb {Z})$ 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 $C^*(PSL(2,\mathbb {Z}))$.

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