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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The full group C$^*$-algebra of the modular group is primitive
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by Erik Bédos and Tron Å. Omland PDF
Proc. Amer. Math. Soc. 140 (2012), 1403-1411 Request permission

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
  • MR Author ID: 930118
  • Email: tronanen@math.ntnu.no
  • 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
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 140 (2012), 1403-1411
  • MSC (2010): Primary 46L05; Secondary 22D25, 46L55
  • DOI: https://doi.org/10.1090/S0002-9939-2011-11143-2
  • MathSciNet review: 2869125