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dc.contributor.authorJacobsen, Karin Marie
dc.contributor.authorJørgensen, Peter
dc.date.accessioned2019-12-17T11:11:19Z
dc.date.available2019-12-17T11:11:19Z
dc.date.created2018-12-13T15:35:07Z
dc.date.issued2019
dc.identifier.citationJournal of Algebra. 2019, 512 114-136.nb_NO
dc.identifier.issn0021-8693
dc.identifier.urihttp://hdl.handle.net/11250/2633604
dc.description.abstractLet 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.abstractd-abelian quotients of (d+2)-angulated categoriesnb_NO
dc.language.isoengnb_NO
dc.publisherElseviernb_NO
dc.relation.urihttps://arxiv.org/abs/1712.07851
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internasjonal*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/deed.no*
dc.titled-abelian quotients of (d+2)-angulated categoriesnb_NO
dc.typeJournal articlenb_NO
dc.typePeer reviewednb_NO
dc.description.versionacceptedVersionnb_NO
dc.source.pagenumber114-136nb_NO
dc.source.volume512nb_NO
dc.source.journalJournal of Algebranb_NO
dc.identifier.doi10.1016/j.jalgebra.2018.11.019
dc.identifier.cristin1642906
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.unitcode194,63,15,0
cristin.unitnameInstitutt for matematiske fag
cristin.ispublishedtrue
cristin.fulltextpostprint
cristin.qualitycode2


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Attribution-NonCommercial-NoDerivatives 4.0 Internasjonal
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