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Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Quantum isometry groups of $0$-dimensional manifolds
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by Jyotishman Bhowmick, Debashish Goswami and Adam Skalski PDF
Trans. Amer. Math. Soc. 363 (2011), 901-921 Request permission

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
  • MR Author ID: 705797
  • ORCID: 0000-0003-1661-8369
  • Email: a.skalski@lancaster.ac.uk
  • Received by editor(s): August 1, 2008
  • Received by editor(s) in revised form: May 7, 2009
  • Published electronically: September 21, 2010
  • © Copyright 2010 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 363 (2011), 901-921
  • MSC (2010): Primary 58B32; Secondary 81R50, 81R60, 46L87
  • DOI: https://doi.org/10.1090/S0002-9947-2010-05141-4
  • MathSciNet review: 2728589