Deformation of algebras associated with group cocycles

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Noncommutative Geometry Pub Date : 2023-09-18 DOI:10.4171/jncg/522

Makoto Yamashita

引用次数: 14

Abstract

We study deformation of algebras with coaction symmetry of reduced algebras of discrete groups, where the deformation parameter is givenby a continuous family of group $2$-cocycles. When the group satisfies the Baum--Connes conjecture with coefficients, we obtain an isomorphism of K-groups of the deformed algebras. This extends both the $\theta$-deformation of Rieffel on $\mathbb{T}^n$-actions, and a recent result of Echterhoff, Lück, Phillips, and Walters on the K-groups on the twisted group algebras.

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群环代数的变形

研究了离散群约化代数中具有共作用对称的代数的变形，其中变形参数由群$2$-环的连续族给出。当群满足带系数的Baum—Connes猜想时，我们得到了变形代数k群的一个同构。这扩展了Rieffel在$\mathbb{T}^n$-作用上的$\theta$-变形，以及Echterhoff, l k, Phillips和Walters关于扭曲群代数上k -群的最新结果。

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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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.