We examine the structure of two possible candidates of isometry groups for the spectral triples on AF-algebras introduced by Christensen and Ivan. In particular, we completely determine the isometry group introduced by Park and observe that these groups coincide in the case of the Cantor set. We also show that the construction of spectral triples on crossed products given by Hawkins, Skalski, White, and Zacharias is suitable for the purpose of lifting isometries.
On isometries of spectral triples associated to AF-algebras and crossed products / Bassi, J.; Conti, R.. - In: JOURNAL OF NONCOMMUTATIVE GEOMETRY. - ISSN 1661-6952. - 18:2(2024), pp. 547-566. [10.4171/JNCG/535]
On isometries of spectral triples associated to AF-algebras and crossed products
Bassi J.;Conti R.
2024
Abstract
We examine the structure of two possible candidates of isometry groups for the spectral triples on AF-algebras introduced by Christensen and Ivan. In particular, we completely determine the isometry group introduced by Park and observe that these groups coincide in the case of the Cantor set. We also show that the construction of spectral triples on crossed products given by Hawkins, Skalski, White, and Zacharias is suitable for the purpose of lifting isometries.| File | Dimensione | Formato | |
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