Geodesic
Derived equivalences between skew-gentle algebras using orbifolds
Documenta mathematica, Tome 27 (2022), pp. 933-982.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Skew-gentle algebras are skew-group algebras of gentle algebras equipped with a certain $\mathbb{Z}_2$-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. \par We prove the compatibility of the $\mathbb{Z}_2$-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.
Classification : 16G20, 16E35, 57R18
Keywords: derived equivalence, skew-gentle algebra, surface dissection, orbifold 
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     title = {Derived equivalences between skew-gentle algebras using orbifolds},
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Amiot, Claire; Brüstle, Thomas. Derived equivalences between skew-gentle algebras using orbifolds. Documenta mathematica, Tome 27 (2022), pp. 933-982. http://geodesic.mathdoc.fr/item/DOCMA_2022__27__a42/