On τ-Tilting Theory and Perpendicular Categories
On τ-Tilting Theory and Perpendicular Categories
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dc.contributor.advisor | Schröer, Jan | |
dc.contributor.author | Ricke, Charlotte | |
dc.date.accessioned | 2020-04-22T22:40:49Z | |
dc.date.available | 2020-04-22T22:40:49Z | |
dc.date.issued | 04.11.2016 | |
dc.identifier.uri | https://hdl.handle.net/20.500.11811/6887 | |
dc.description.abstract | We extend the classification of finitely generated modules and the combinatorial description of Auslander-Reiten sequences for finite-dimensional string algebras to infinite dimensional completed string algebras. The proof of the classification of the finitely generated modules is based on work by Crawley-Boevey. Using the combinatorics of strings we prove that mutation of finitely generated support tau-tilting pairs is possible for completed string algebras. Furthermore, we study perpendicular categories for 1-Iwanaga-Gorenstein algebras. We prove that for finite-dimensional 1-Iwanaga-Gorenstein algebras the perpendicular category of an indecomposable partial tilting module satisfying certain conditions is again equivalent to a module category over a 1-Iwanaga-Gorenstein algebra. We apply and generalize this result for a special class of algebras which were recently introduced by Geiß, Leclerc and Schöer. These algebras are 1-Iwanaga-Gorenstein algebras defined via quivers with relations associated with symmetrizable Cartan matrices. | |
dc.language.iso | eng | |
dc.rights | In Copyright | |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | |
dc.subject.ddc | 510 Mathematik | |
dc.title | On τ-Tilting Theory and Perpendicular Categories | |
dc.type | Dissertation oder Habilitation | |
dc.publisher.name | Universitäts- und Landesbibliothek Bonn | |
dc.publisher.location | Bonn | |
dc.rights.accessRights | openAccess | |
dc.identifier.urn | https://nbn-resolving.org/urn:nbn:de:hbz:5n-44802 | |
ulbbn.pubtype | Erstveröffentlichung | |
ulbbnediss.affiliation.name | Rheinische Friedrich-Wilhelms-Universität Bonn | |
ulbbnediss.affiliation.location | Bonn | |
ulbbnediss.thesis.level | Dissertation | |
ulbbnediss.dissID | 4480 | |
ulbbnediss.date.accepted | 12.09.2016 | |
ulbbnediss.institute | Mathematisch-Naturwissenschaftliche Fakultät : Fachgruppe Mathematik / Mathematisches Institut | |
ulbbnediss.fakultaet | Mathematisch-Naturwissenschaftliche Fakultät | |
dc.contributor.coReferee | Burban, Igor |
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