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Dessins d’Enfants and Brauer Configuration Algebras

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Galois Covers, Grothendieck-Teichmüller Theory and Dessins d'Enfants (GGT-DE 2018)

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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 of 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 algebra of a dessin d’enfant and its dual share the same path algebra.

This work has been supported through the EPSRC Early Career Fellowship EP/P016294/1 for the second author and the University of Leicester.

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Acknowledgements

The first author would like to thank the University of Leicester for hospitality during his stays at Leicester.

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Authors and Affiliations

  1. Department of Computer Science, Smith College, Northampton, MA, 01063, USA

    Goran Malić

  2. Department of Mathematics, University of Leicester, University Road, Leicester, LE1 7RH, UK

    Sibylle Schroll

Authors
  1. Goran Malić
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  2. Sibylle Schroll
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Corresponding author

Correspondence to Goran Malić .

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Editors and Affiliations

  1. Pure Mathematics Group, School of Mathematics and Actuarial Science, University of Leicester, Leicester, Leicestershire, UK

    Frank Neumann

  2. Pure Mathematics Group, School of Mathematics and Actuarial Science, University of Leicester, Leicester, Leicestershire, UK

    Sibylle Schroll

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Malić, G., Schroll, S. (2020). Dessins d’Enfants and Brauer Configuration Algebras. In: Neumann, F., Schroll, S. (eds) Galois Covers, Grothendieck-Teichmüller Theory and Dessins d'Enfants. GGT-DE 2018. Springer Proceedings in Mathematics & Statistics, vol 330. Springer, Cham. https://doi.org/10.1007/978-3-030-51795-3_10

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