Higher Auslander Algebras of Finite Representation Type

IF 0.6 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2026-01-24 DOI:10.1007/s10468-025-10373-2

Shen Li

引用次数: 0

Abstract

Let \(\Lambda \) be a higher Auslander algebra with global dimension \(n+1\). In this paper, we prove that \(\Lambda \) is representation-finite if and only if the number of non-isomorphic indecomposable \(\Lambda \)-modules with projective dimension \(n+1\) is finite. As an application, we classify the representation-finite higher Auslander algebras of linearly oriented type \(\mathbb {A}\) in the sense of Iyama and calculate the number of non-isomorphic indecomposable modules over these algebras.

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有限表示型的高等Auslander代数

设\(\Lambda \)为全局维数为\(n+1\)的高等澳洲代数。本文证明了\(\Lambda \)是表示有限的当且仅当具有射影维数\(n+1\)的非同构不可分解的\(\Lambda \) -模的数量有限。作为应用，我们在Iyama意义上对线性定向型\(\mathbb {A}\)的表示有限高Auslander代数进行了分类，并计算了这些代数上的非同构不可分解模的个数。

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.