The dynamical Cuntz semigroup and ideal-free quotients of Cuntz semigroups

IF 1.1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2025-07-10 DOI:10.1016/j.laa.2025.07.006

Joan Bosa , Francesc Perera , Jianchao Wu , Joachim Zacharias

引用次数: 0

Abstract

We develop a theory of general quotients for W- and Cu-semigroups beyond the case of quotients by ideals. To this end, we introduce the notion of a normal pair, which allows us to take quotients of W-semigroups in a similar way as normal subgroups arise as kernels of group homomorphisms.

We use this to define the dynamical Cuntz semigroup as the universal object induced from an action of a group G on a W-semigroup. In the C*-algebraic framework, under mild assumptions, the universality of this dynamical invariant helps us tap into the structure of the Cuntz semigroup of crossed product C*-algebras.

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动态孔茨半群与孔茨半群的无理想商

在理想商的情况下，我们发展了W-和cu -半群的一般商理论。为此，我们引入正规对的概念，它允许我们以类似于作为群同态核的正规子群的方式取w -半群的商。利用这一点，我们将动态Cuntz半群定义为群G作用于w -半群所诱导出的普遍对象。在C*-代数框架中，在温和的假设下，这一动态不变量的普适性有助于我们深入研究交叉积C*-代数的Cuntz半群的结构。

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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来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.