A NOTE ON PROJECTIONS IN ÉTALE GROUPOID ALGEBRAS AND DIAGONAL-PRESERVING HOMOMORPHISMS

IF 0.6 4区数学 Q3 MATHEMATICS

Bulletin of the Australian Mathematical Society Pub Date : 2024-02-29 DOI:10.1017/s0004972724000042

BENJAMIN STEINBERG

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引用次数: 0

Abstract

Carlsen [‘

$\ast $

-isomorphism of Leavitt path algebras over

$\Bbb Z$

’, Adv. Math.324 (2018), 326–335] showed that any

$\ast $

-homomorphism between Leavitt path algebras over

$\mathbb Z$

is automatically diagonal preserving and hence induces an isomorphism of boundary path groupoids. His result works over conjugation-closed subrings of

$\mathbb C$

enjoying certain properties. In this paper, we characterise the rings considered by Carlsen as precisely those rings for which every

$\ast $

-homomorphism of algebras of Hausdorff ample groupoids is automatically diagonal preserving. Moreover, the more general groupoid result has a simpler proof.

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关于埃塔莱群集代数中的投影和对角保全同态的注释

卡尔森（Carlsen）[' $\ast $ -isomorphism of Leavitt path algebras over $\Bbb Z$ ', Adv. Math.324 (2018), 326-335]表明，在$\mathbb Z$上的Leavitt路径代数之间的任何$\ast $ -同构都是自动对角保全的，因此会诱导边界路径群的同构。他的结果适用于$\mathbb C$的共轭封闭子环，并享有某些性质。在本文中，我们将卡尔森所考虑的环描述为这样的环：对于这些环，豪斯多夫充裕类群的每一个 $\ast $ -同构都自动地对角保全。此外，更一般的类群结果有一个更简单的证明。

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

Bulletin of the Australian Mathematical Society 数学-数学

CiteScore

1.20

自引率

14.30%

发文量

149

审稿时长

4-8 weeks

期刊介绍： Bulletin of the Australian Mathematical Society aims at quick publication of original research in all branches of mathematics. Papers are accepted only after peer review but editorial decisions on acceptance or otherwise are taken quickly, normally within a month of receipt of the paper. The Bulletin concentrates on presenting new and interesting results in a clear and attractive way. Published Bi-monthly Published for the Australian Mathematical Society