Lifting spectral triples to noncommutative principal bundles

Abstract

Given a free action of a compact Lie group $G$ on a unital C*-algebra $\mathcal{A}$ and a spectral triple on the corresponding fixed point algebra ${\mathcal{A}}^G$, we present a systematic and in-depth construction of a spectral triple on $\mathcal{A}$ that is build upon the geometry of ${\mathcal{A}}^G$ and $G$. We compare our construction with a selection of established examples.

References in corpus (6)

• Why the Standard Model
• Noncommutative Geometry Approach to Principal and Associated Bundles
• Dynamical Systems on Spectral Metric Spaces
• Freeness of actions of finite groups on C*-algebras
• Factorisation of equivariant spectral triples in unbounded KK-theory
• Index theory for actions of compact Lie groups on C*-algebras

Cited by in corpus (4)

• Geometric foundations for classical $\mathrm{U}(1)$-gauge theory on noncommutative manifolds
• A Note on Twisted Crossed Products and Spectral Triples
• An Atiyah Sequence for Noncommutative Principal Bundles
• Realizations of free actions via their fixed point algebras