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arXiv · 1406.4642

Crossed product extensions of spectral triples

Bruno Iochum·Thierry Masson
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Abstract

Given a spectral triple $(A,H,D)$ and a $C^*$-dynamical system $(\mathbf{A}, G, \alpha)$ where $A$ is dense in $\mathbf{A}$ and $G$ is a locally compact group, we extend the triple to a triplet $(\mathcal{B},\mathcal{H},\mathcal{D})$ on the crossed product $G \ltimes_{\alpha, \text{red}} \mathbf{A}$ which can be promoted to a modular-type twisted spectral triple within a general procedure exemplified by two cases: the $C^*$-algebra of the affine group and the conformal group acting on a complete Riemannian spin manifold.

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Bruno Iochum, Thierry Masson. 2014-06-18. Crossed product extensions of spectral triples. https://arxiv.org/abs/1406.4642

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