Quantum metrics on crossed products with groups of polynomial growth
Year: 2024
Type: preprint
Abstract: 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 K K KK -theory and show that it arises as an internal Kasparov product of unbounded Kasparov modules.
DOI: 10.1090/tran/9340
Authors: Are Austad, Jens Kaad, David Kyed
Institutions: University of Oslo, University of Southern Denmark
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4404952668