Journal of Noncommutative Geometry

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Volume 10, Issue 1, 2016, pp. 65–133
DOI: 10.4171/JNCG/229

Published online: 2016-03-22

Crossed product extensions of spectral triples

Bruno Iochum[1] and Thierry Masson[2]

(1) Aix-Marseille Université, France
(2) Aix-Marseille Université, France

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 $(\mathcal {B, H,D})$ on the crossed product $G \ltimes_{\alpha, \mathrm {red}} \mathbf A$ 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.

Keywords: Twisted spectral triple, dynamical system, crossed product, modular operator, affine and conformal groups

Iochum Bruno, Masson Thierry: Crossed product extensions of spectral triples. J. Noncommut. Geom. 10 (2016), 65-133. doi: 10.4171/JNCG/229