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Auslander-Reiten theory in triangulated categories

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Publication date
2014
Author(s)
Niu, Hongwei
Subject
Auslander-Reiten theory
 
Triangulated categories
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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.
URI
http://hdl.handle.net/11143/5455
Collection
  • Moissonnage BAC [3168]
  • Sciences – Mémoires [1602]

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