Quantum differentials of Spectral triples, Dirichlet spaces and discrete groups

Fabio E. G. Cipriani; Jean-Luc Sauvageot

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arXiv · 2301.00140

Quantum differentials of Spectral triples, Dirichlet spaces and discrete groups

Fabio E. G. Cipriani·Jean-Luc Sauvageot

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Abstract

We study natural conditions on essentially discrete spectral triples by which the quantum differential $da$ belongs to the ideal generated by the unit length $ds=D^{-1}$. We also study upper and lower bounds on the singular values of the $da$'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.

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BibTeX RIS

Fabio E. G. Cipriani, Jean-Luc Sauvageot. 2022-12-31. Quantum differentials of Spectral triples, Dirichlet spaces and discrete groups. https://arxiv.org/abs/2301.00140

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