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.
Keywords
Cite
@article{arxiv.1908.05509,
title = {Dessins d'enfants and Brauer configuration algebras},
author = {Goran Malić and Sibylle Schroll},
journal= {arXiv preprint arXiv:1908.05509},
year = {2019}
}
Comments
20 pages, to appear in the Proceedings of the LMS workshop 'Galois covers, Grothendieck-Teichmueller theory and dessins d'enfants', Springer Proceedings in Mathematics & Statistics. This paper contains a short survey of dessins d'enfants and Brauer configuration algebras as well as new results