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

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.

36 pages. We improved the first version substantially with a section on the deformation of the quantum isometry group. Notational and other errors are corrected

References in corpus (2)

• Quantum Group of Isometries in Classical and Noncommutative Geometry
• Quantum Isometry Groups of Noncommutative Manifolds Obtained by Deformation Using Dual Unitary 2-Cocycles