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## A note on the injectivity of actions of compact quantum groups on a class of $C^{\ast }$-algebras

### Volume 120 / 2020

Banach Center Publications 120 (2020), 71-79 MSC: 81R50, 81R60, 20G42, 58B34. DOI: 10.4064/bc120-6

#### Abstract

We give some sufficient conditions for the injectivity of actions of compact quantum groups on $C^{\ast }$-algebras. As an application, we prove that any faithful smooth action by a compact quantum group on a compact smooth (not necessarily connected) manifold is injective. A similar result is proved for actions on $C^{\ast }$-algebras obtained by Rieffel deformations of compact, smooth manifolds.

#### Authors

• Debashish GoswamiIndian Statistical Institute
Kolkata 700108, India
e-mail
• Soumalya JoardarIndian Statistical Institute
203, B. T. Road, Kolkata 700108, India
ORCID: 0000-0002-8405-4967
e-mail

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