强拟局部代数及其$K$-理论

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Noncommutative Geometry Pub Date : 2021-08-02 DOI:10.4171/jncg/499

HengDa Bao, Xiaoman Chen, Jiawen Zhang

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引用次数: 3

摘要

本文引入了强拟局部代数的概念。它们被定义为每一个具有有界几何的离散度量空间，并且位于Roe代数和准局部代数之间。我们证明了强拟局部代数是粗糙不变量，因此编码了底层空间的粗糙几何信息。我们证明了对于一个允许粗嵌入到Hilbert空间的具有有界几何的离散度量空间，将Roe代数包含到强拟局部代数中可以在K -理论中导出一个同构。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Strongly quasi-local algebras and their $K$-theories

In this paper, we introduce a notion of strongly quasi-local algebras. They are defined for each discrete metric space with bounded geometry, and sit between the Roe algebra and the quasi-local algebra. We show that strongly quasi-local algebras are coarse invariants, hence encoding coarse geometric information of the underlying spaces. We prove that for a discrete metric space with bounded geometry which admits a coarse embedding into a Hilbert space, the inclusion of the Roe algebra into the strongly quasi-local algebra induces an isomorphism in $K$-theory.

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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.