Spectral triples on crossed products arising from equicontinuous actions

Details Spectral triples on crossed products arising from equicontinuous actions Spectral triples on crossed products arising from equicontinuous actions

2011-03-31

arxiv.org/abs/1103.6199v3

Mathematics

Operator Algebras

19 pages (v3 adds a discussion of the equicontinuity condition and expands the examples section)

Scientific paper

The external Kasparov product is used to construct odd and even spectral triples on crossed products of C*-algebras by actions of discrete groups which are equicontinuous in a natural (topological) sense. When the group in question is Z this gives another viewpoint on the spectral triples introduced by Belissard, Marcolli and Reihani. We investigate the properties of this construction and apply it to produce spectral triples on the Bunce-Deddens algebra arising from the odometer action on the Cantor set and some other crossed products of AF-algebras.

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