Abstract
AbstractIn 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.
Funder
Engineering and Physical Sciences Research Council
Publisher
Springer Science and Business Media LLC
Reference25 articles.
1. Adachi, T., Aihara, T., Chan, A.: Classification of two-term tilting complexes over Brauer graph algebras. Math. Z. 290(1–2), 1–36 (2018)
2. Assem, I, Simson, D, Skowroński, A.: Elements of the representation theory of associative algebras. Vol. 1. Techniques of representation theory. London Mathematical Society Student Texts, 65. Cambridge University Press, Cambridge, (2006)
3. Belyĭ, G.V.: On galois extensions of a maximal cyclotomic field. Math. USSR Izvestija 14, 247–256 (1980)
4. Belyĭ, G.V.: A new proof of the three point theorem. Sb. Math. 193(3–4), 329–332 (2002)
5. Benson, D.: Representations and cohomology. I. Basic representation theory of finite groups and associative algebras. Cambridge Studies in Advanced Mathematics, 30. Cambridge University Press, Cambridge (1998)