Deformations of spectral triples and their quantum isometry groups via monoidal equivalences

TL;DR

This paper introduces a novel deformation method for spectral triples and their quantum isometry groups using monoidal equivalences, extending previous cocycle deformation techniques.

Contribution

It generalizes the cocycle deformation approach to spectral triples and quantum isometry groups through monoidal equivalences and fiber functors.

Findings

Provides a new deformation framework for spectral triples

Extends cocycle deformation to a broader setting

Enables new constructions of quantum isometry groups

Abstract

In this paper, we propose a new procedure to deform spectral triples and their quantum isometry groups. The deformation data are a spectral triple $(\mathcal A,\mathcal H, D)$, a compact quantum group $\mathbb G$ acting algebraically and by orientation-preserving isometries on $(\mathcal A,\mathcal H,D)$ and a unitary fiber functor $\psi$ on $\mathbb G$. The deformation procedure is a genuine generalization of the cocycle deformation of Goswami and Joardar.