[HTML][HTML] Higher Auslander–Reiten sequences and t-structures
JC Arias, E Backelin - Journal of Algebra, 2016 - Elsevier
Let R be an artin algebra and C an additive subcategory of mod (R). We construct a t-
structure on the homotopy category K−(C) and argue that its heart HC is a natural domain for …
structure on the homotopy category K−(C) and argue that its heart HC is a natural domain for …
Indecomposable injective functors from an abelian category to the category of abelian groups
K Yamagata - Communications in Algebra, 1979 - Taylor & Francis
Let C be an abelian category. Then for any object C in C,~ xt'(C,) is defined as a covariant
functor from C to Ab such that for each X in C EX~'(C, X) is an additive group consisting of …
functor from C to Ab such that for each X in C EX~'(C, X) is an additive group consisting of …
The Auslander-Reiten theory of the morphism category of projective modules
R Hafezi, J Wei - arXiv preprint arXiv:2307.10715, 2023 - arxiv.org
We investigate the structure of certain almost split sequences in $\mathcal {P}(\Lambda) $,
ie, the category of morphisms between projective modules over an Artin algebra $\Lambda …
ie, the category of morphisms between projective modules over an Artin algebra $\Lambda …
Some remarks on reflection functors
N Marmaridis - Representations of Algebras: Proceedings of the Third …, 1981 - Springer
Recently Sheila Brenner and MCR Butler [7J have studied, the so ca. lled tilting functors,
which are a generalisation of the Berns. tein-Gelfand-Ponomarev reflection functors. Their …
which are a generalisation of the Berns. tein-Gelfand-Ponomarev reflection functors. Their …
The left and the right parts of a module category
In this paper, we study, for an artin algebra, the class LA (and RA) which is a full subcategory
of the category modA of finitely generated A-modules, and which consists of all …
of the category modA of finitely generated A-modules, and which consists of all …
Categorical resolutions of a class of derived categories
P Zhang - Science China Mathematics, 2018 - Springer
We clarify the relation between the subcategory D hf b (A) of homological finite objects in D b
(A) and the subcategory K b (P) of perfect complexes in D b (A), by giving two classes of …
(A) and the subcategory K b (P) of perfect complexes in D b (A), by giving two classes of …
Auslander–Reiten triangles in homotopy categories
Y Zheng, Z Huang - Communications in Algebra, 2016 - Taylor & Francis
Let A be an artin algebra. We show that the bounded homotopy category of finitely
generated right A-modules has Auslander–Reiten triangles. Two applications are given:(1) …
generated right A-modules has Auslander–Reiten triangles. Two applications are given:(1) …
[引用][C] Extensions of homologically finite subcategories
SA Sikko, SO Smalø - Archiv der Mathematik, 1993 - Springer
Introduction. The study of homologically finite subcategories has turned out to be important
in several contexts, especially in the representation theory of artin algebras. In this paper we …
in several contexts, especially in the representation theory of artin algebras. In this paper we …
Syzygy properties under recollements of derived categories
K Wu, J Wei - Journal of Algebra, 2022 - Elsevier
Abstract Let A, B and C be artin algebras such that there is a recollement of D (Mod A)
relative to D (Mod B) and D (Mod C). We compare the algebras A, B and C with respect to …
relative to D (Mod B) and D (Mod C). We compare the algebras A, B and C with respect to …
Auslander Reiten conjecture and functor Jk2
JY Guo - Archiv der Mathematik, 1998 - infona.pl
Recently, Auslander and Reiten initiated the study of k-Gorenstein artin algebra. They
conjectured that if an artin algebra $\it\Lambda $ is k-Gorenstein for all k, then it is …
conjectured that if an artin algebra $\it\Lambda $ is k-Gorenstein for all k, then it is …