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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Quantum isometry groups of 0-dimensional manifolds


Authors: Jyotishman Bhowmick, Debashish Goswami and Adam Skalski
Journal: Trans. Amer. Math. Soc. 363 (2011), 901-921
MSC (2010): Primary 58B32; Secondary 81R50, 81R60, 46L87
Published electronically: September 21, 2010
MathSciNet review: 2728589
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Abstract: Quantum isometry groups of spectral triples associated with approximately finite-dimensional $ C^*$-algebras are shown to arise as inductive limits of quantum symmetry groups of corresponding truncated Bratteli diagrams. This is used to determine explicitly the quantum isometry group of the natural spectral triple on the algebra of continuous functions on the middle-third Cantor set. It is also shown that the quantum symmetry groups of finite graphs or metric spaces coincide with the quantum isometry groups of the corresponding classical objects equipped with natural Laplacians.


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Additional Information

Jyotishman Bhowmick
Affiliation: Stat-Math Unit, Indian Statistical Institute, 203, B. T. Road, Kolkata 700 208, India
Address at time of publication: ICTP, Mathematics Section, Strada Costiera 11, I-34151, Trieste, Italy
Email: jyotish_r@isical.ac.in, jbhowmic@ictp.it

Debashish Goswami
Affiliation: Stat-Math Unit, Indian Statistical Institute, 203, B. T. Road, Kolkata 700 208, India
Email: goswamid@isical.ac.in

Adam Skalski
Affiliation: Department of Mathematics, University of Łódź, ul. Banacha 22, 90-238 Łódź, Poland
Address at time of publication: Department of Mathematics and Statistics, Lancaster University, Lancaster, LA1 4YF, United Kingdom
Email: a.skalski@lancaster.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9947-2010-05141-4
PII: S 0002-9947(2010)05141-4
Keywords: Compact quantum group, quantum isometry groups, spectral triples, $AF$ algebras
Received by editor(s): August 1, 2008
Received by editor(s) in revised form: May 7, 2009
Published electronically: September 21, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.