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Lifting spectral triples to noncommutative principal bundles (2012.15364v2)
Published 30 Dec 2020 in math.OA, math-ph, math.DG, and math.MP
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.