Module Categories of Small Radical Nilpotency

IF 0.5 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2023-07-24 DOI:10.1007/s10468-023-10211-3

Shiping Liu, Youqi Yin

引用次数: 0

Abstract

This paper aims to initiate a study of the representation theory of representation-finite artin algebras in terms of the nilpotency of the radical of their module category. Firstly, we shall calculate this nilpotency explicitly for hereditary algebras of type \(\mathbb {A}_n\) and for Nakayama algebras. Surprisingly, this nilpotency for a given algebra coincides with its Loewy length if and only if the algebra is a hereditary Nakayama algebra. Secondly, we shall find all artin algebras for which this nilpotency is equal to any given positive integer up to four and describe completely their module category.

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小根幂零的模范畴

本文旨在从表征有限阿尔丁代数的模类的基的零势出发，展开对表征有限阿尔丁代数的表征理论的研究。首先，我们将明确地计算类型为 \(\mathbb {A}_n\) 的遗传代数和中山代数的零势。令人惊讶的是，当且仅当给定代数是遗传中山代数时，该代数的零势与它的洛维长度重合。其次，我们将找到这个零势等于任意给定的正整数（最多为四）的所有阿尔金代数，并完整地描述它们的模类。

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.