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ISSN 1088-6826(e) ISSN 0002-9939(p)

Quantum isometry group of the -tori

Author(s): Jyotishman Bhowmick
Journal: Proc. Amer. Math. Soc. 137 (2009), 3155-3161.
MSC (2000): Primary 58B32; Secondary 16W30, 46L87, 46L89
Posted: May 4, 2009
MathSciNet review: 2506475
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Abstract: We show that the quantum isometry group (introduced by Goswami) of the -tori $\mathbb{T}^{n}$ coincides with its classical isometry group; i.e. there does not exist any faithful isometric action on $\mathbb{T}^{n}$ by a genuine (noncommutative as a $C^{\ast}$ -algebra) compact quantum group. Moreover, using an earlier result, we conclude that the quantum isometry group of the noncommutative tori is a Rieffel deformation of the quantum isometry group of the commutative -tori.

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Additional Information:

Jyotishman Bhowmick
Affiliation: Stat-Math Unit, Kolkata Centre, Indian Statistical Institute, 203, B. T. Road, Kolkata 700 108, India
Email: jyotish_r@isical.ac.in

DOI: 10.1090/S0002-9939-09-09908-0
PII: S 0002-9939(09)09908-0
Received by editor(s): May 6, 2008
Posted: May 4, 2009
Additional Notes: Support from the National Board of Higher Mathematics, India, is gratefully acknowledged
Communicated by: Varghese Mathai
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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