In 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.
| Identifer | oai:union.ndltd.org:usherbrooke.ca/oai:savoirs.usherbrooke.ca:11143/5455 |
| Date | January 2014 |
| Creators | Niu, Hongwei |
| Contributors | Liu, Shiping, Smith, David |
| Publisher | Université de Sherbrooke |
| Source Sets | Université de Sherbrooke |
| Language | English |
| Detected Language | English |
| Type | Mémoire |
| Rights | © Hongwei Niu |
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