Dessins D’Enfants, Brauer Graph Algebras and Galois Invariants

IF 0.5 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2023-09-18 DOI:10.1007/s10468-023-10232-y

Goran Malić, Sibylle Schroll

引用次数: 0

Abstract

In this paper, we associate a finite dimensional algebra, called a Brauer graph algebra, to every clean dessin d’enfant by constructing a quiver based on the monodromy of the dessin. We show that Galois conjugate dessins d’enfants give rise to derived equivalent Brauer graph algebras and that the stable Auslander-Reiten quiver and the dimension of the Brauer graph algebra are invariant under the induced action of the absolute Galois group.

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Dessins D'Enfants、Brauer Graph Algebras 和 Galois Invariants

在本文中，我们通过构建一个基于 "雏形 "单色性的四元组，将一个有限维代数（称为布劳尔图代数）与每一个干净的 "雏形 "相关联。我们证明，伽罗瓦共轭的 d'enfants 会产生派生等价的 Brauer 图代数，而且稳定的 Auslander-Reiten quiver 和 Brauer 图代数的维数在绝对伽罗瓦群的诱导作用下是不变的。

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.