On Spectral Triples on Crossed Products Arising From Equicontinuous Actions

  • A. Hawkins
  • A. Skalski
  • S. White
  • J. Zacharias

Abstract

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 sense. When the group in question is $\mathsf{Z}$ 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.
Published
2013-12-01
How to Cite
Hawkins, A., Skalski, A., White, S., & Zacharias, J. (2013). On Spectral Triples on Crossed Products Arising From Equicontinuous Actions. MATHEMATICA SCANDINAVICA, 113(2), 262-291. https://doi.org/10.7146/math.scand.a-15572
Section
Articles