Deformation of Spectral Triples and Their Quantum Isometry Groups

Abstract

This chapter deals with \( \mathrm{QISO}^{\mathcal{L}} \) and \( \mathrm{QISO}^{+}_R \) of a cocycle twisted noncommutative manifold. We first discuss the cocycle deformation of compact quantum groups, von Neumann algebras and spectral triples, followed by the proof of the fact that \( \mathrm{QISO}^{+}_{R} \) and \( \mathrm{QISO}^{\mathcal{L}} \) of a cocycle twist of a (noncommutative) manifold is a cocycle twist of the \( \mathrm{QISO}^{+}_R \) and \( \mathrm{QISO}^{\mathcal{L}} \) (respectively) of the original (undeformed) manifold.