Universität zu Köln

Labardini-Fragoso, Daniel, Schroll, Sibylle ORCID: 0000-0001-9618-7647 and Valdivieso, Yadira (2022). Derived categories of skew-gentle algebras and orbifolds. Glasg. Math. J., 64 (3). S. 649 - 675. NEW YORK: CAMBRIDGE UNIV PRESS. ISSN 1469-509X

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Abstract

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 Grobner 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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Labardini-Fragoso, Daniel UNSPECIFIED UNSPECIFIED UNSPECIFIED Schroll, Sibylle UNSPECIFIED orcid.org/0000-0001-9618-7647 UNSPECIFIED Valdivieso, Yadira UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-674061
DOI:	10.1017/S0017089521000422
Journal or Publication Title:	Glasg. Math. J.
Volume:	64
Number:	3
Page Range:	S. 649 - 675
Date:	2022
Publisher:	CAMBRIDGE UNIV PRESS
Place of Publication:	NEW YORK
ISSN:	1469-509X
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language SINGULARITY CATEGORIES; SURFACES; INDECOMPOSABLES; QUIVERS Multiple languages Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/67406