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, France
  • Thomas 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
Derived equivalences between skew-gentle algebras using orbifolds cover
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Skew-gentle algebras are skew-group algebras of gentle algebras equipped with a certain Z2\mathbb{Z}_2-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 Z2\mathbb{Z}_2-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