Derived equivalences between skew-gentle algebras using orbifolds - CNRS - Centre national de la recherche scientifique
Article Dans Une Revue Documenta Mathematica Année : 2022

Derived equivalences between skew-gentle algebras using orbifolds

Résumé

Gentle algebras are in bijection with admissible dissections of marked oriented surfaces. In this paper, we further study the properties of admissible dissections and we show that silting objects for gentle algebras are given by admissible dissections of the associated surface. We associate to each gentle algebra a line field on the corresponding surface and prove that the derived equivalence class of the algebra is completely determined by the homotopy class of the line field up to homeomorphism of the surface. Then, based on winding numbers and the Arf invariant of a certain quadratic form over $${\mathbb {Z}}_2$$ Z 2 , we translate this to a numerical complete derived invariant for gentle algebras.

Dates et versions

hal-04708008 , version 1 (24-09-2024)

Identifiants

Citer

Thomas Brüstle, Claire Amiot. Derived equivalences between skew-gentle algebras using orbifolds. Documenta Mathematica, 2022, 27 (2), pp.933-982. ⟨10.4171/DM/889⟩. ⟨hal-04708008⟩
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