Exceptional sequences in the derived category of a gentle algebra
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Wen Chang [1] ; Sibylle Schroll [2]
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[1] Shaanxi Normal University
Shaanxi Normal University
China
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[2] University of Cologne
University of Cologne
Kreisfreie Stadt Köln, Alemania
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- Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 29, Nº. 3, 2023
- Idioma: inglés
- Enlaces
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Resumen
In this paper, using the correspondence of gentle algebras and dissections of marked surfaces, we study full exceptional sequences in the perfect derived category Kb(A) of a gentle algebra A. We show that full exceptional sequences in Kb(A) exist if and only if the associated marked surface has no punctures and has at least two marked points on the boundary. Furthermore, by using induction on cuts of surfaces, we characterize when an exceptional sequence can be completed to a full exceptional sequence. If the genus of the associated surface is zero then we show that the action of the braid group together with the grading shift on full exceptional sequences in Kb(A) is transitive. For the case of surfaces of higher genus, we reduce the problem of transitivity to the problem of the existence of certain sequences of pairs of exceptional objects. Finally, we interpret the duality of a full exceptional sequence induced by the longest element in the associated symmetric group using Koszul duality.
