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 alg...
AbstractWe use t-structures on the homotopy category Kb(R-mod) for an artin algebra R and Wattsʼ rep...
AbstractLet a : 0→A→B→R→0 be the Auslander-Reiten sequence for the trivial module R over a group alg...
Let $\mathscr{C}$ be a $(d+2)$-angulated category with $d$-suspension functor $\Sigma^d$. Our main r...
In this dissertation, let B be a triangulated category and let D be an extension-closed subcategory...
Ph. D. Thesis.Auslander-Reiten theory plays an important role in the study of abelian and triangulat...
PhD thesisChapter 0 gives a gentle background to the thesis. It begins with some general notions an...
We rst introduce the notion of an Auslander-Reiten sequence in a Krull-Schmidt category. This uni es...
Neste trabalho, apresentamos uma prova da existência de triângulos de Auslander-Reiten(TAR) para obj...
Abstract. We develop an Auslander-Reiten theory for triangulated categories which is based on Brown’...
AbstractA class of triangulated categories with a finiteness condition is singled out. These triangu...
Abstract. This paper studies Auslander-Reiten triangles in sub-categories of triangulated categories...
The notion of an extriangulated category gives a unification of existing theories in exact or abelia...
By the knitting technique introduced to build the Auslander-Reiten quiver of the category of complex...
Krause H. AUSLANDER–REITEN TRIANGLES AND A THEOREM OF ZIMMERMANN. Bulletin of the London Mathematica...
We investigate (existence of) Auslander–Reiten triangles in a triangulated category in con-nection w...
AbstractWe use t-structures on the homotopy category Kb(R-mod) for an artin algebra R and Wattsʼ rep...
AbstractLet a : 0→A→B→R→0 be the Auslander-Reiten sequence for the trivial module R over a group alg...
Let $\mathscr{C}$ be a $(d+2)$-angulated category with $d$-suspension functor $\Sigma^d$. Our main r...
In this dissertation, let B be a triangulated category and let D be an extension-closed subcategory...
Ph. D. Thesis.Auslander-Reiten theory plays an important role in the study of abelian and triangulat...
PhD thesisChapter 0 gives a gentle background to the thesis. It begins with some general notions an...
We rst introduce the notion of an Auslander-Reiten sequence in a Krull-Schmidt category. This uni es...
Neste trabalho, apresentamos uma prova da existência de triângulos de Auslander-Reiten(TAR) para obj...
Abstract. We develop an Auslander-Reiten theory for triangulated categories which is based on Brown’...
AbstractA class of triangulated categories with a finiteness condition is singled out. These triangu...
Abstract. This paper studies Auslander-Reiten triangles in sub-categories of triangulated categories...
The notion of an extriangulated category gives a unification of existing theories in exact or abelia...
By the knitting technique introduced to build the Auslander-Reiten quiver of the category of complex...
Krause H. AUSLANDER–REITEN TRIANGLES AND A THEOREM OF ZIMMERMANN. Bulletin of the London Mathematica...
We investigate (existence of) Auslander–Reiten triangles in a triangulated category in con-nection w...
AbstractWe use t-structures on the homotopy category Kb(R-mod) for an artin algebra R and Wattsʼ rep...
AbstractLet a : 0→A→B→R→0 be the Auslander-Reiten sequence for the trivial module R over a group alg...
Let $\mathscr{C}$ be a $(d+2)$-angulated category with $d$-suspension functor $\Sigma^d$. Our main r...