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dc.contributor.advisorLiu, Shiping
dc.contributor.advisorSmith, David
dc.contributor.authorNiu, Hongweifr
dc.date.accessioned2014-09-04T13:36:07Z
dc.date.available2014-09-04T13:36:07Z
dc.date.created2014fr
dc.date.issued2014-09-04
dc.identifier.urihttp://hdl.handle.net/11143/5455
dc.description.abstractIn this dissertation, let B be a triangulated category and let D be an extension-closed subcategory of B. First, we give some new characterizations of an Auslander-Reiten triangle in D, which yields some necessary and sufficient conditions for D to have Auslander-Reiten triangles. Next, we study when an Auslander-Reiten triangle in B induces an Auslander-Reiten triangle in D. As an application, we study Auslander-Reiten triangles in a triangulated category with a t-structure. In case the t-structure has a t-hereditary heart, we establish the connection between the Auslander-Reiten triangles in B and the Auslander-Reiten sequences in the heart. Finally, we specialize to the bounded derived category of all modules of a noetherian algebra over a complete local noetherian commutative ring. Our result generalizes the corresponding result of Happel’s in the bounded derived category of finite dimensional modules of a finite dimensional algebra over an algebraically closed field.fr
dc.language.isoengfr
dc.publisherUniversité de Sherbrookefr
dc.rights© Hongwei Niufr
dc.subjectAuslander-Reiten theoryfr
dc.subjectTriangulated categoriesfr
dc.titleAuslander-Reiten theory in triangulated categoriesfr
dc.typeMémoirefr
tme.degree.disciplineMathématiquesfr
tme.degree.grantorFaculté des sciencesfr
tme.degree.levelMaîtrisefr
tme.degree.nameM. Sc.fr


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