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Dessins d'enfants, Brauer graph algebras and Galois invariants

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arxiv 1902.09876 v3 pith:RJINMLTF submitted 2019-02-26 math.RT math.CO

Goran Malic , Sibylle Schroll This is my paper · ORCID
classification math.RTmath.CO
keywords brauergraphalgebragaloisalgebrasdessindessinsenfants
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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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  1. Dessins d'enfants and Brauer configuration algebras

    math.RT 2019-08 conditional novelty 5.0 of 10

    Associating Brauer configuration algebras to dessins d'enfants yields numerical invariants, algebra dimension and centre dimension, claimed to be invariant under the absolute Galois group.

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