A Note on Singularity Categories and Triangular Matrix Algebras

IF 0.5 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2024-01-06 DOI:10.1007/s10468-023-10249-3

Yongyun Qin

引用次数: 0

Abstract

Let \(\Lambda = \left[ \begin{array}{cc} A &{} 0 \\ M &{} B \end{array}\right] \) be an Artin algebra and \(_BM_A\) a B-A-bimodule. We prove that there is a triangle equivalence \(D_{sg}(\Lambda ) \cong D_{sg}(A)\coprod D_{sg}(B)\) between the corresponding singularity categories if \(_BM\) is semi-simple and \(M_A\) is projective. As a result, we obtain a new method for describing the singularity categories of certain bounded quiver algebras.

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奇异性类别和三角矩阵代数的说明

让 \(\Lambda = \left[ \begin{array}{cc} A &{} 0 \\M &{} B \end{array}\right] \)是一个阿汀代数，而 \(_BM_A\) 是一个 B-A 二模子。我们证明，如果 \(_BM\) 是半简单的，并且 \(M_A\) 是投影的，那么相应的奇异范畴之间存在三角等价关系 \(D_{sg}(\Lambda ) \cong D_{sg}(A)\coprod D_{sg}(B)\)。因此，我们得到了描述某些有界四元组的奇点范畴的新方法。

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

Algebras and Representation Theory 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Algebras and Representation Theory features carefully refereed papers relating, in its broadest sense, to the structure and representation theory of algebras, including Lie algebras and superalgebras, rings of differential operators, group rings and algebras, C*-algebras and Hopf algebras, with particular emphasis on quantum groups. The journal contains high level, significant and original research papers, as well as expository survey papers written by specialists who present the state-of-the-art of well-defined subjects or subdomains. Occasionally, special issues on specific subjects are published as well, the latter allowing specialists and non-specialists to quickly get acquainted with new developments and topics within the field of rings, algebras and their applications.