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Existence and Rigidity of Quantum Isometry Groups for Compact Metric Spaces


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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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).

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