Quantum isometry group of the $n$-tori
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- by Jyotishman Bhowmick PDF
- Proc. Amer. Math. Soc. 137 (2009), 3155-3161 Request permission
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.References
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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
- 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
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2506475