具有几乎分离关系的 Quipu Quivers 和 Nakayama Algebras

IF 0.5 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2023-12-12 DOI:10.1007/s10468-023-10247-5

Didrik Fosse

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引用次数: 0

摘要

具有几乎独立关系的中山代数是指任何一对关系之间的重叠最多只有一个箭头。在本文中，我们给出了这种中山代数与一种特殊形式的四元组路径代数之间的等价性。此外，我们还展示了如何利用这一推导等价关系来产生一个具有几乎独立关系的线性中山代数的完整分类。作为一个应用，我们列出了所有长度为 \(\le 8\) 的、具有几乎独立关系的中山代数的派生等价类。

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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Quipu Quivers and Nakayama Algebras with Almost Separate Relations

A Nakayama algebra with almost separate relations is one where the overlap between any pair of relations is at most one arrow. In this paper we give a derived equivalence between such Nakayama algebras and path algebras of quivers of a special form known as quipu quivers. Furthermore, we show how this derived equivalence can be used to produce a complete classification of linear Nakayama algebras with almost separate relations. As an application, we include a list of the derived equivalence classes of all Nakayama algebras of length \(\le 8\) with almost separate relations.

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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.