Crossed products as compact quantum metric spaces
| Autor: | Klisse, Mario |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | By employing the external Kasparov product, Hawkins, Skalski, White and Zacharias constructed spectral triples on crossed product C$^\ast$-algebras by equicontinuous actions of discrete groups. They further raised the question for whether their construction turns the respective crossed product into a compact quantum metric space in the sense of Rieffel. By introducing the concept of groups separated with respect to a given length function, we give an affirmative answer in the case of virtually Abelian groups equipped with certain orbit metric length functions. We further complement our results with a discussion of natural examples such as generalized Bunce-Deddens algebras and higher-dimensional non-commutative tori. Comment: 28 pages, v2: typos corrected, Accepted by Canadian Journal of Mathematics |
| Databáze: | arXiv |
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