Quantum Isometry Groups of Noncommutative Manifolds Obtained by Deformation Using Dual Unitary 2-Cocycles

TL;DR

This paper proves that the quantum isometry group of a noncommutative manifold deformed by a dual unitary 2-cocycle is isomorphic to a twisted deformation of the original quantum isometry group, generalizing previous results.

Contribution

It establishes a general isomorphism between quantum isometry groups of deformed and original spectral triples using dual unitary 2-cocycles.

Findings

Quantum isometry groups are preserved under dual unitary 2-cocycle deformation.

The isomorphism extends previous results on Rieffel deformation.

Provides a framework for understanding symmetries in deformed noncommutative geometries.

Abstract

It is proved that the (volume and orientation-preserving) quantum isometry group of a spectral triple obtained by deformation by some dual unitary 2-cocycle is isomorphic with a similar twist-deformation of the quantum isometry group of the original (undeformed) spectral triple. This result generalizes similar work by Bhowmick and Goswami for Rieffel-deformed spectral triples in [Comm. Math. Phys. 285 (2009), 421-444, arXiv:0707.2648].