On isometries of spectral triples associated to $\mathrm{AF}$-algebras and crossed products

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Noncommutative Geometry Pub Date : 2023-11-03 DOI:10.4171/jncg/535

Jacopo Bassi, Roberto Conti

引用次数: 1

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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与$\ mathm {AF}$-代数和交叉积相关的谱三元组的等距

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来源期刊

Journal of Noncommutative Geometry 数学-数学

CiteScore

1.60

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Noncommutative Geometry covers the noncommutative world in all its aspects. It is devoted to publication of research articles which represent major advances in the area of noncommutative geometry and its applications to other fields of mathematics and theoretical physics. Topics covered include in particular: Hochschild and cyclic cohomology K-theory and index theory Measure theory and topology of noncommutative spaces, operator algebras Spectral geometry of noncommutative spaces Noncommutative algebraic geometry Hopf algebras and quantum groups Foliations, groupoids, stacks, gerbes Deformations and quantization Noncommutative spaces in number theory and arithmetic geometry Noncommutative geometry in physics: QFT, renormalization, gauge theory, string theory, gravity, mirror symmetry, solid state physics, statistical mechanics.