Universität zu Köln

Haugland, Johanne ORCID: 0000-0003-3128-4715, Jacobsen, Karin M. and Schroll, Sibylle ORCID: 0000-0001-9618-7647 (2022). The role of gentle algebras in higher homological algebra. Forum Math., 34 (5). S. 1255 - 1276. BERLIN: WALTER DE GRUYTER GMBH. ISSN 1435-5337

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Abstract

We investigate the role of gentle algebras in higher homological algebra. In the first part of the paper, we show that if the module category of a gentle algebra Lambda contains a d-cluster tilting subcategory for some d >= 2, then. is a radical square zero Nakayama algebra. This gives a complete classification of weakly d-representation finite gentle algebras. In the second part, we use a geometric model of the derived category to prove a similar result in the triangulated setup. More precisely, we show that if D-b(Lambda) contains a d-cluster tilting subcategory that is closed under [ d], then Lambda is derived equivalent to an algebra of Dynkin type A. Furthermore, our approach gives a geometric characterization of all d-cluster tilting subcategories of D-b(Lambda) that are closed under [d].

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Haugland, Johanne UNSPECIFIED orcid.org/0000-0003-3128-4715 UNSPECIFIED Jacobsen, Karin M. UNSPECIFIED UNSPECIFIED UNSPECIFIED Schroll, Sibylle UNSPECIFIED orcid.org/0000-0001-9618-7647 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-673285
DOI:	10.1515/forum-2021-0311
Journal or Publication Title:	Forum Math.
Volume:	34
Number:	5
Page Range:	S. 1255 - 1276
Date:	2022
Publisher:	WALTER DE GRUYTER GMBH
Place of Publication:	BERLIN
ISSN:	1435-5337
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language REPRESENTATION-FINITE ALGEBRAS; TILTED ALGEBRAS; STABLE CATEGORIES; AUSLANDER; EXTENSIONS; MODULES Multiple languages Mathematics, Applied; Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/67328