Spectral triples for higher-rank graph $C^*$-algebras
Operator Algebras
2018-04-17 v1 Differential Geometry
Abstract
In this note, we present a new way to associate a spectral triple to the noncommutative -algebra of a strongly connected finite higher-rank graph . We generalize a spectral triple of Consani and Marcolli from Cuntz-Krieger algebras to higher-rank graph -algebras , and we prove that these spectral triples are intimately connected to the wavelet decomposition of the infinite path space of which was introduced by Farsi, Gillaspy, Kang, and Packer in 2015. In particular, we prove that the wavelet decomposition of Farsi et al. describes the eigenspaces of the Dirac operator of this spectral triple.
Cite
@article{arxiv.1804.05209,
title = {Spectral triples for higher-rank graph $C^*$-algebras},
author = {Carla Farsi and Elizabeth Gillaspy and Antoine Julien and Sooran Kang and Judith Packer},
journal= {arXiv preprint arXiv:1804.05209},
year = {2018}
}
Comments
This paper is a partial replacement of arXiv:1701.05321; the latter will not be submitted for publication