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
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: |
|
||||||||||||||||
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: |
|
||||||||||||||||
URI: | http://kups.ub.uni-koeln.de/id/eprint/67328 |
Downloads
Downloads per month over past year
Altmetric
Export
Actions (login required)
![]() |
View Item |