A note on the centralizer of a subalgebra of the Steinberg algebra

IF 0.7 4区数学 Q2 MATHEMATICS

St Petersburg Mathematical Journal Pub Date : 2021-12-28 DOI:10.1090/spmj/1695

R. Hazrat, Huanhuan Li

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引用次数: 2

Abstract

For an ample Hausdorff groupoid G \mathcal {G} , and the Steinberg algebra A R ( G ) A_R(\mathcal {G}) with coefficients in the commutative ring R R with unit, the centralizer is described for the subalgebra A R ( U ) A_R(U) with U U an open closed invariant subset of the unit space of G \mathcal {G} . In particular, it is shown that the algebra of the interior of the isotropy is indeed the centralizer of the diagonal subalgebra of the Steinberg algebra. This will unify several results in the literature, and the corresponding results for Leavitt path algebras follow.

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关于Steinberg代数的一个子代数的扶正器的注记

对于一个例子的Hausdorff群G \mathcal {G}，以及在交换环R R中具有系数的Steinberg代数A R(G) A_R(\mathcal {G})，描述了子代数A R(U) A_R(U)具有U U是G \mathcal {G}的单位空间的开闭不变子集的正化器。特别地，证明了各向同性内部的代数确实是Steinberg代数对角线子代数的中心化器。这将统一文献中的几个结果，并给出莱维特路径代数的相应结果。

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

St Petersburg Mathematical Journal MATHEMATICS-

CiteScore

1.00

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.