Some remarks on the action of Quantum Isometry Groups

TL;DR

This paper establishes a new condition on spectral triples that guarantees the quantum isometry group acts as a $C^*$-action on the algebra, advancing understanding of quantum symmetries in noncommutative geometry.

Contribution

It introduces a novel sufficient condition for quantum isometry groups to act as $C^*$-actions on spectral triples.

Findings

Provides a new criterion for $C^*$-actions of quantum isometry groups

Enhances understanding of quantum symmetries in spectral triples

Bridges spectral triple conditions with quantum group actions

Abstract

We give a new sufficient condition on a spectral triple to ensure that the quantum group of orientation and volume preserving isometries defined in \cite{qorient} has a $C^*$-action on the underlying $C^*$ algebra.