English

Quantum differentials of Spectral triples, Dirichlet spaces and discrete groups

Operator Algebras 2023-01-03 v1 Mathematical Physics Functional Analysis math.MP

Abstract

We study natural conditions on essentially discrete spectral triples by which the quantum differential dada belongs to the ideal generated by the unit length ds=D1ds=D^{-1}. We also study upper and lower bounds on the singular values of the dada's and apply the general framework to natural spectral triples of Dirichlet spaces and, in particular, those on dual of discrete groups arising from negative definite functions.

Keywords

Cite

@article{arxiv.2301.00140,
  title  = {Quantum differentials of Spectral triples, Dirichlet spaces and discrete groups},
  author = {Fabio E. G. Cipriani and Jean-Luc Sauvageot},
  journal= {arXiv preprint arXiv:2301.00140},
  year   = {2023}
}