Coactions and skew products for topological quivers

IF 0.7 3区 数学 Q2 MATHEMATICS
Lucas Hall
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引用次数: 0

Abstract

Given a cocycle on a topological quiver by a locally compact group, the author constructs a skew product topological quiver and determines conditions under which a topological quiver can be identified as a skew product. We investigate the relationship between the ${C^*}$ -algebra of the skew product and a certain native coaction on the ${C^*}$ -algebra of the original quiver, finding that the crossed product by the coaction is isomorphic to the skew product. As an application, we show that the reduced crossed product by the dual action is Morita equivalent to the ${C^*}$ -algebra of the original quiver.
拓扑四元组的共生和倾斜积
给定局部紧密群在拓扑簇上的循环,作者构建了一个斜积拓扑簇,并确定了拓扑簇可以被识别为斜积的条件。我们研究了斜积的 ${C^*}$ - 代数与原簇的 ${C^*}$ - 代数上的某个本征协效之间的关系,发现协效的交叉积与斜积同构。作为应用,我们证明了对偶作用的还原交叉积与原始簇的 ${C^*}$ - 代数是莫里塔等价的。
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
CiteScore
1.10
自引率
0.00%
发文量
49
审稿时长
6 months
期刊介绍: The Edinburgh Mathematical Society was founded in 1883 and over the years, has evolved into the principal society for the promotion of mathematics research in Scotland. The Society has published its Proceedings since 1884. This journal contains research papers on topics in a broad range of pure and applied mathematics, together with a number of topical book reviews.
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