Corrigendum to “Mapping cones for morphisms involving a band complex in the bounded derived category of a gentle algebra” [J. Algebra 530 (2019) 163–194]

Çanakçı, ̛İlke; Pauksztello, David; Schroll, Sibylle

doi:10.1016/j.jalgebra.2020.08.005

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2023

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“…From the point of view of homological algebra, the class of gentle algebras is of particular interest, since it is closed under derived equivalence [45]. Their derived categories are well-understood [6,13,16,17,19,20,31]. Moreover, in [12], Avella-Alaminos and Geiss introduced a numerical derived invariant distinguishing between many derived equivalence classes of gentle algebras.…”

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confidence: 99%

A complete derived invariant for gentle algebras via winding numbers and Arf invariants

Amiot

Plamondon

Schroll

2023

Sel. Math. New Ser.

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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.

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