On isometries of spectral triples associated to AF-algebras and crossed products

Jacopo Bassi; Roberto Conti

doi:10.4171/JNCG/535

On isometries of spectral triples associated to AF-algebras and crossed products

Jacopo Bassi, Roberto Conti

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English
Pages (from-to)	547-566
Number of pages	20
Journal	Journal of Noncommutative Geometry
Volume	18
Issue number	2
DOIs	https://doi.org/10.4171/JNCG/535
State	Published - 1 Jan 2024
Externally published	Yes

Keywords

AF-algebra
Cantor set
Dirac operator
crossed product
isometry group
non-commutative geometry

ASJC Scopus subject areas

Algebra and Number Theory
Mathematical Physics
Geometry and Topology

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10.4171/JNCG/535

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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.",

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AU - Conti, Roberto

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AB - 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.

KW - AF-algebra

KW - Cantor set

KW - Dirac operator

KW - crossed product

KW - isometry group

KW - non-commutative geometry

UR - https://www.scopus.com/pages/publications/85188463030

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DO - 10.4171/JNCG/535

M3 - Article

AN - SCOPUS:85188463030

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ER -

On isometries of spectral triples associated to AF-algebras and crossed products

Abstract

Keywords

ASJC Scopus subject areas

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