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 | References | Similar Articles | Additional Information

Abstract: Quantum isometry groups of spectral triples associated with approximately finite-dimensional -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:
https://doi.org/10.1090/S0002-9947-2010-05141-4

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.