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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Authors: Erik Bédos and Tron Å. Omland
Journal: Proc. Amer. Math. Soc. 140 (2012), 1403-1411
MSC (2010): Primary 46L05; Secondary 22D25, 46L55
Published electronically: August 10, 2011
MathSciNet review: 2869125
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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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Additional Information

Erik Bédos
Affiliation: Institute of Mathematics, University of Oslo, P.O. Box 1053 Blindern, 0316 Oslo, Norway
Email: bedos@math.uio.no

Tron Å. Omland
Affiliation: Department of Mathematical Sciences, Norwegian University of Science and Technology, 7491 Trondheim, Norway
Email: tronanen@math.ntnu.no

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11143-2
PII: S 0002-9939(2011)11143-2
Received by editor(s): January 6, 2010
Received by editor(s) in revised form: January 7, 2011
Published electronically: August 10, 2011
Additional Notes: Both authors are partially supported by the Norwegian Research Council (NFR)
Dedicated: This paper is dedicated to the memory of Gerard J. Murphy
Communicated by: Marius Junge
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.