Non-existence of faithful isometric action of compact quantum groups on compact, connected Riemannian manifolds

Authors

Debashish Goswami, Indian Statistical Institute, Kolkata
Soumalya Joardar, Jawaharlal Nehru Centre for Advanced Scientific Research

Article Type

Research Article

Publication Title

Geometric and Functional Analysis

Abstract

Suppose that a compact quantum group Q acts faithfully on a smooth, compact, connected manifold M, i.e. has a C* (co)-action α on C(M), such that the action α is isometric in the sense of [GOS09] for some Riemannian structure on M. We prove that Q must be commutative as a C* algebra i.e. Q≅ C(G) for some compact group G acting smoothly on M. In particular, the quantum isometry group of M (in the sense of [GOS09]) coincides with C(ISO(M)).

First Page

146

Last Page

178

DOI

10.1007/s00039-018-0437-z

Publication Date

2-1-2018

Comments

All Open Access, Green

Recommended Citation

Goswami, Debashish and Joardar, Soumalya, "Non-existence of faithful isometric action of compact quantum groups on compact, connected Riemannian manifolds" (2018). Journal Articles. 1488.
https://digitalcommons.isical.ac.in/journal-articles/1488