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Proceedings of the American Mathematical Society

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

 

 

Quantum isometry group of the $ n$-tori


Author: Jyotishman Bhowmick
Journal: Proc. Amer. Math. Soc. 137 (2009), 3155-3161
MSC (2000): Primary 58B32; Secondary 16W30, 46L87, 46L89
DOI: https://doi.org/10.1090/S0002-9939-09-09908-0
Published electronically: May 4, 2009
MathSciNet review: 2506475
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Abstract: We show that the quantum isometry group (introduced by Goswami) of the $ n$-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 $ n$ tori is a Rieffel deformation of the quantum isometry group of the commutative $ n$-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: https://doi.org/10.1090/S0002-9939-09-09908-0
Received by editor(s): May 6, 2008
Published electronically: May 4, 2009
Additional Notes: Support from the National Board of Higher Mathematics, India, is gratefully acknowledged
Communicated by: Varghese Mathai
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.