| dc.description.abstract | 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. | fr |
