Derived categories of skew-gentle algebras and orbifolds

Skew-gentle algebras are a generalisation of the well-known class of gentle algebras with which they share many common properties. In this work, using non-commutative Gröbner basis theory, we show that these algebras are strong Koszul and that the Koszul dual is again skew-gentle. We give a geometri...

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Bibliographic Details
Published inGlasgow mathematical journal Vol. 64; no. 3; pp. 649 - 674
Main Authors Labardini-Fragoso, Daniel, Schroll, Sibylle, Valdivieso, Yadira
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.09.2022
Subjects
Algebra
Categories
Classification
Dissection
Geometry
Homology
Mathematics
05E10
16G20
16G10
05E99
16E35
18E30
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Summary:Skew-gentle algebras are a generalisation of the well-known class of gentle algebras with which they share many common properties. In this work, using non-commutative Gröbner basis theory, we show that these algebras are strong Koszul and that the Koszul dual is again skew-gentle. We give a geometric model of their bounded derived categories in terms of polygonal dissections of surfaces with orbifold points, establishing a correspondence between curves in the orbifold and indecomposable objects. Moreover, we show that the orbifold dissections encode homological properties of skew-gentle algebras such as their singularity categories, their Gorenstein dimensions and derived invariants such as the determinant of their q-Cartan matrices.
ISSN:0017-0895
1469-509X
DOI:10.1017/S0017089521000422