Crossed product extensions of spectral triples

2014/06/18 by Bruno Iochum, Iochum, Bruno, Thierry Masson +1
Mathematics · #22D25 #46L55 #46Lxx #54H15 #58B34 #FOS: Mathematics #Operator Algebras (math.OA) #math.OA #msc:22D25 #msc:46L55 #msc:46Lxx #msc:54H15 #msc:58B34

paper · pdf · doi:10.48550/arxiv.1406.4642

Version 3: version to appear in Journal of Noncommutative Geometry

arxiv created 2015/11/25 · arxiv updated 2015/11/26

Abstract

Given a spectral triple (A,H,D) and a C^*-dynamical system (A, G, α) where A is dense in A and G is a locally compact group, we extend the triple to a triplet (B,H,D) on the crossed product G \ltimes_{α, red} 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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