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Existence and Rigidity of Quantum Isometry Groups for Compact Metric Spaces

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Abstract

We prove the existence of a quantum isometry groups for new classes of metric spaces: (i) geodesic metrics for compact connected Riemannian manifolds (possibly with boundary) and (ii) metric spaces admitting a uniformly distributed probability measure. In the former case it also follows from recent results of the second author that the quantum isometry group is classical, i.e. the commutative \(C^*\)-algebra of continuous functions on the Riemannian isometry group.

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Authors and Affiliations

  1. Department of Mathematics, University at Buffalo, Buffalo, NY, 14260-2900, USA

    Alexandru Chirvasitu

  2. Indian Statistical Institute, 203, B. T. Road, Kolkata, 700108, India

    Debashish Goswami

Authors
  1. Alexandru Chirvasitu
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  2. Debashish Goswami
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Correspondence to Debashish Goswami.

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Communicated by Y. Kawahigashi

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A. Chirvasitu Partially supported by NSF Grant DMS-1801011.

D. Goswami Partially supported by J.C. Bose Fellowship from D.S.T. (Govt. of India).

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Chirvasitu, A., Goswami, D. Existence and Rigidity of Quantum Isometry Groups for Compact Metric Spaces. Commun. Math. Phys. 380, 723–754 (2020). https://doi.org/10.1007/s00220-020-03849-3

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