dc.contributor.author | Jacobsen, Karin Marie | |
dc.contributor.author | Jørgensen, Peter | |
dc.date.accessioned | 2019-12-17T11:11:19Z | |
dc.date.available | 2019-12-17T11:11:19Z | |
dc.date.created | 2018-12-13T15:35:07Z | |
dc.date.issued | 2019 | |
dc.identifier.citation | Journal of Algebra. 2019, 512 114-136. | nb_NO |
dc.identifier.issn | 0021-8693 | |
dc.identifier.uri | http://hdl.handle.net/11250/2633604 | |
dc.description.abstract | Let T be a triangulated category. If t is a cluster tilting object and I=add t is the ideal of morphisms factoring through an object of add t, then the quotient category T/I is abelian. This is an important result of cluster theory, due to Keller–Reiten and König–Zhu. More general conditions which imply that T/I is abelian were determined by Grimeland and the first author. Now let T be a suitable (d+2)-angulated category for an integer d>=0. If t is a cluster tilting object in the sense of Oppermann–Thomas and I=add t is the ideal of morphisms factoring through an object of add t, then we show that T/I is d-abelian. The notions of (d+2)-angulated and d-abelian categories are due to Geiss–Keller–Oppermann and Jasso. They are higher homological generalisations of triangulated and abelian categories, which are recovered in the special case d=1. We actually show that if A is the endomorphism algebra of t, then T/I is equivalent to a d-cluster tilting subcategory of mod A in the sense of Iyama; this implies that T/I is d-abelian. Moreover, we show that Γ is a d-Gorenstein algebra. More general conditions which imply that T/I is d-abelian will also be determined, generalising the triangulated results of Grimeland and the first author. | nb_NO |
dc.description.abstract | d-abelian quotients of (d+2)-angulated categories | nb_NO |
dc.language.iso | eng | nb_NO |
dc.publisher | Elsevier | nb_NO |
dc.relation.uri | https://arxiv.org/abs/1712.07851 | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internasjonal | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/deed.no | * |
dc.title | d-abelian quotients of (d+2)-angulated categories | nb_NO |
dc.type | Journal article | nb_NO |
dc.type | Peer reviewed | nb_NO |
dc.description.version | acceptedVersion | nb_NO |
dc.source.pagenumber | 114-136 | nb_NO |
dc.source.volume | 512 | nb_NO |
dc.source.journal | Journal of Algebra | nb_NO |
dc.identifier.doi | 10.1016/j.jalgebra.2018.11.019 | |
dc.identifier.cristin | 1642906 | |
dc.description.localcode | © 2018. This is the authors’ accepted and refereed manuscript to the article. Locked until 29.11.2020 due to copyright restrictions. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/ | nb_NO |
cristin.unitcode | 194,63,15,0 | |
cristin.unitname | Institutt for matematiske fag | |
cristin.ispublished | true | |
cristin.fulltext | postprint | |
cristin.qualitycode | 2 | |