Dessins d'enfants and Brauer configuration algebras

Abstract

In this paper we associate to a dessin d'enfant an associative algebra, called a Brauer configuration algebra. This is an algebra given by quiver and relations induced by the monodromy of the dessin d'enfant. We show that the dimension of the Brauer configuration algebra associated to a dessin d'enfant and the dimension of the centre this algebra are invariant under the action of the absolute Galois group. We give some examples of well-known algebras and their dessins d'enfants. Finally we show that the Brauer configuration algebras of a dessin d'enfant and its dual share the same path algebra.