Dessins D'Enfants、Brauer Graph Algebras 和 Galois Invariants

Pub Date : 2023-09-18 DOI:10.1007/s10468-023-10232-y

Goran Malić, Sibylle Schroll

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引用次数: 0

摘要

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。

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Dessins D’Enfants, Brauer Graph Algebras and Galois Invariants

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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