Abstract
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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Acknowledgements
We thank the anonymous referee for carefully reading the manuscript. Their comments and suggestions have improved the quality and clarity of the paper.
Funding
Open Access funding enabled and organized by Projekt DEAL. Most of this work has been carried out while the second author was working at the University of Leicester and it has been supported through the EPSRC Early Career Fellowship EP/P016294/1. The first author thanks the University of Leicester for their hospitality. The second author would also like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme ’Cluster Algebras and Representation Theory’ where part of the work on this paper was undertaken. This work was supported by EPSRC grant EP/R014604/1
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Malić, G., Schroll, S. Dessins D’Enfants, Brauer Graph Algebras and Galois Invariants. Algebr Represent Theor 27, 655–665 (2024). https://doi.org/10.1007/s10468-023-10232-y
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DOI: https://doi.org/10.1007/s10468-023-10232-y
Keywords
- Dessins d’enfants
- Galois invariant
- Absolute Galois group
- Finite dimensional algebra
- Brauer graph algebra
- Derived equivalence