On spectral triples on crossed products arising from equicontinuous actions
Operator Algebras
2015-08-28 v4
Abstract
The external Kasparov product is used to construct odd and even spectral triples on crossed products of -algebras by actions of discrete groups which are equicontinuous in a natural sense. When the group in question is 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.
Keywords
Cite
@article{arxiv.1103.6199,
title = {On spectral triples on crossed products arising from equicontinuous actions},
author = {Andrew Hawkins and Adam Skalski and Stuart White and Joachim Zacharias},
journal= {arXiv preprint arXiv:1103.6199},
year = {2015}
}
Comments
22 pages (v4 corrects a mistake in the discussion of the equicontinuity condition and modifies the terminology used). The paper will appear in Mathematica Scandinavica