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ЖУРНАЛЫ // Алгебра и анализ // Архив

Алгебра и анализ, 2021, том 33, выпуск 1, страницы 246–253 (Mi aa1744)

Эта публикация цитируется в 1 статье

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

R. Hazrata, Huanhuan Lib

a Centre for Research in Mathematics and Data Sceince, Western Sydney University, Australia
b School of Mathematical Sciences, Anhui University, Hefei 230601, Anhui, PR China

Аннотация: For an ample Hausdorff groupoid $\mathcal{G}$, and the Steinberg algebra $A_R(\mathcal{G})$ with coefficients in the commutative ring $R$ with unit, we describe the centralizer of the subalgebra $A_R(U)$ with $U$ an open closed invariant subset of the unit space of $\mathcal{G}$. 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.

Ключевые слова: ample groupoid, Steinberg algebra, centralizer, Leavitt path algebra, diagonal of the Leavitt path algebra, commutative core of the Leavitt path algebra.

Поступила в редакцию: 23.03.2020

Язык публикации: английский


 Англоязычная версия: St. Petersburg Mathematical Journal, 2022, 33:1, 179–184


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