Derived equivalences between skew-gentle algebras using orbifolds
Claire Amiot
Institut Universitaire de France, Université Grenoble Alpes, Institut Fourier, 100 rue des maths, 38402 Saint Martin d'Hères, FranceThomas Brüstle
Bishop's University, 2600 College Street, Sherbrooke QC J1M 1Z7, Canada, and Université de Sherbrooke, 2500, boul. de l'Université, Sherbrooke QC J1K 2R1, Canada
Abstract
Skew-gentle algebras are skew-group algebras of gentle algebras equipped with a certain -action. Building on the bijective correspondence between gentle algebras and dissected surfaces, we obtain in this paper a bijection between skew-gentle algebras and certain dissected orbifolds that admit a double cover.
We prove the compatibility of the -action on the double cover with the skew-group algebra construction. This allows us to investigate the derived equivalence relation between skew-gentle algebras in geometric terms: We associate to each skew-gentle algebra a line field on the orbifold, and on its double cover, and interpret different kinds of derived equivalences of skew-gentle algebras in terms of diffeomorphisms respecting the homotopy class of the line fields associated to the algebras.
Cite this article
Claire Amiot, Thomas Brüstle, Derived equivalences between skew-gentle algebras using orbifolds. Doc. Math. 27 (2022), pp. 933–982
DOI 10.4171/DM/889