Existence and rigidity of quantum isometry groups for compact metric spaces
Quantum Algebra
2020-10-28 v2 Differential Geometry
Functional Analysis
Operator Algebras
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 -algebra of continuous functions on the Riemannian isometry group.
Keywords
Cite
@article{arxiv.1902.09732,
title = {Existence and rigidity of quantum isometry groups for compact metric spaces},
author = {Alexandru Chirvasitu and Debashish Goswami},
journal= {arXiv preprint arXiv:1902.09732},
year = {2020}
}
Comments
30 pages + references; edits after referee comments; to appear in Communications in Mathematical Physics