Quantum metrics on crossed products with groups of polynomial growth

Fuente: arXiv
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Bibliographic Details
Main Authors: Austad, Are, Kaad, Jens, Kyed, David
Format: Preprint
Published: 2023
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author Austad, Are
Kaad, Jens
Kyed, David
author_facet Austad, Are
Kaad, Jens
Kyed, David
contents We show how to equip the crossed product between a group of polynomial growth and a compact quantum metric space with a compact quantum metric space structure. When the quantum metric on the base space arises from a spectral triple, which is compatible with the action of the group, we furthermore show that the crossed product becomes a spectral metric space. Lastly, we analyse the spectral triple at the crossed product level from the point of view of unbounded $KK$-theory and show that it arises as an internal Kasparov product of unbounded Kasparov modules.
format Preprint
id arxiv_https___arxiv_org_abs_2312_12220
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Quantum metrics on crossed products with groups of polynomial growth
Austad, Are
Kaad, Jens
Kyed, David
Operator Algebras
58B34, 47L65, 46L55
We show how to equip the crossed product between a group of polynomial growth and a compact quantum metric space with a compact quantum metric space structure. When the quantum metric on the base space arises from a spectral triple, which is compatible with the action of the group, we furthermore show that the crossed product becomes a spectral metric space. Lastly, we analyse the spectral triple at the crossed product level from the point of view of unbounded $KK$-theory and show that it arises as an internal Kasparov product of unbounded Kasparov modules.
title Quantum metrics on crossed products with groups of polynomial growth
topic Operator Algebras
58B34, 47L65, 46L55
url https://arxiv.org/abs/2312.12220