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On the Koszulity of some quiver algebras
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Algebra and Geometry.
2016 (English)Licentiate thesis, comprehensive summary (Other academic)
Place, publisher, year, edition, pages
Uppsala: Uppsala University, 2016. , 38 p.
Series
U.U.D.M. report / Uppsala University, Department of Mathematics, ISSN 1101-3591 ; 2016:4
National Category
Algebra and Logic
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-303527OAI: oai:DiVA.org:uu-303527DiVA: diva2:972210
Presentation
2016-10-11, Häggsalen, Ångströmlaboratoriet, Uppsala, 13:15
Opponent
Supervisors
Available from: 2016-09-22 Created: 2016-09-20 Last updated: 2016-09-22Bibliographically approved
List of papers
1. Koszulity of some path categories
Open this publication in new window or tab >>Koszulity of some path categories
2017 (English)In: Communications in Algebra, ISSN 0092-7872, E-ISSN 1532-4125, Vol. 45, no 9, 4084-4092 p.Article in journal (Refereed) Published
Abstract [en]

We prove Koszulity of certain linear path categories obtained from connected graphs with some infinite directed walk. These categories can be viewed as locally quadratic dual to preprojective algebras.

Place, publisher, year, edition, pages
Taylor & Francis, 2017
Keyword
Koszul algebras
National Category
Algebra and Logic
Research subject
Mathematics
Identifiers
urn:nbn:se:uu:diva-303546 (URN)10.1080/00927872.2016.1260727 (DOI)000399458900033 ()
Available from: 2016-09-20 Created: 2016-09-20 Last updated: 2017-05-30Bibliographically approved
2. Incidence category of the Young lattice, injections between finite sets, and Koszulity
Open this publication in new window or tab >>Incidence category of the Young lattice, injections between finite sets, and Koszulity
(English)Article in journal (Other academic) Submitted
Abstract [en]

We study the quadratic quotients of the incidence category of the Young lattice defined using the zero relations corresponding to adding two boxes to the same row, or to the same column or both. We show that the latter quotient corresponds to the Koszul dual of the original incidence category while the first two quotients are, in a natural way, Koszul duals of each other, hence they are in particular Koszul self-dual. Both of these two quotients are known to be basic representatives in the Morita equivalence class of the category of injections between finite sets. We also present a new, rather direct, argument establishing this Morita equivalence.

National Category
Algebra and Logic
Research subject
Mathematics
Identifiers
urn:nbn:se:uu:diva-303704 (URN)
Available from: 2016-09-22 Created: 2016-09-22 Last updated: 2016-09-22

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