共查询到20条相似文献,搜索用时 31 毫秒
1.
An Auslander-Reiten formula for complexes of modules is presented. This formula contains as a special case the classical Auslander-Reiten formula. The Auslander-Reiten translate of a complex is described explicitly, and various applications are discussed. 相似文献
2.
Shengyong Pan 《代数通讯》2013,41(10):3695-3704
In this note, we prove that the generalized Auslander-Reiten conjecture is preserved under derived equivalences between Artin algebras. 相似文献
3.
Deng Ming Xu 《数学学报(英文版)》2013,29(10):1993-1996
It is proved that the Auslander-Reiten conjecture is true for local Artin algebras with radical cube zero. 相似文献
4.
Grzegorz BOBINSKI 《数学学报(英文版)》2007,23(6):1033-1052
The aim of the paper is to classify the indecomposable modules and describe the Auslander-Reiten sequences for the admissible algebras with formal two-ray modules. 相似文献
5.
The Auslander-Reiten quiver of a finite-dimensional associative algebra encodes information about the indecomposable finite-dimensional representations of and their homomorphisms. A component of the Auslander-Reiten quiver is called preprojective if it does not admit oriented cycles and each of its modules can be shifted into a projective module using the Auslander-Reiten translation. Preprojective components play an important role in the present research on algebras of finite and tame representation type. We present an algorithm which detects all preprojective components of a given algebra.
6.
Claudia Chaio 《代数通讯》2017,45(5):1953-1968
We study the degrees of irreducible morphisms between indecomposable modules lying in generalized standard coherent almost cyclic components of Auslander-Reiten quivers of artin algebras. 相似文献
7.
Stable equivalence preserves representation type 总被引:1,自引:0,他引:1
H. Krause 《Commentarii Mathematici Helvetici》1997,72(2):266-284
Given two finite dimensional algebras and , it is shown that is of wild representation type if and only if is of wild representation type provided that the stable categories of finite dimensional modules over and $\Gamma$ are equivalent. The proof uses generic modules. In fact, a stable equivalence induces a bijection between the
isomorphism classes of generic modules over and , and the result follows from certain additional properties of this bijection. In the second part of this paper the Auslander-Reiten
translation is extended to an operation on the category of all modules. It is shown that various finiteness conditions are
preserved by this operation. Moreover, the Auslander-Reiten translation induces a homeomorphism between the set of non-projective
and the set of non-injective points in the Ziegler spectrum. As a consequence one obtains that for an algebra of tame representation
type every generic module remains fixed under the Auslander-Reiten translation.
Received: July 24, 1996 相似文献
8.
We consider a class of algebras whose Auslander-Reiten quivers have starting components that are not generalized standard.
For these components we introduce a generalization of a slice and show that only in finitely many cases (up to isomorphism)
a slice module is a tilting module.
The first named author was supported by the Polish Scientific Grant KBN No 1 P03A 018 27 相似文献
9.
Jaworska Alicja 《Central European Journal of Mathematics》2007,5(4):665-685
Trivial extensions of a certain subclass of minimal 2-fundamental algebras are examined. For such algebras the characterization
of components of the Auslander-Reiten quiver which contain indecomposable projective modules is given.
相似文献
10.
Let A be a finite-dimensional algebra over an algebraically closed field k,E the category of all exact sequences in A-mod,MP(respectively,MI)the full subcategory of E consisting of those objects with projective(respectively,injective)middle terms.It is proved that MP(respectively,MI)is contravariantly finite(respectively,covariantly finite)in E.As an application,it is shown that MP=MI is functorially finite and has Auslander-Reiten sequences provided A is selfinjective. 相似文献
11.
Extriangulated category was introduced by H.Nakaoka and Y.Palu to give a unification of properties in exact categories anjd triangulated categories.A notion of tilting(resp.,cotilting)subcategories in an extriangulated category is defined in this paper.We give a Bazzoni characterization of tilting(resp.,cotilting)subcategories and obtain an Auslander-Reiten correspondence between tilting(resp.,cotilting)subcategories and coresolving covariantly(resp.,resolving contravariantly)finite subcatgories which are closed under direct summands and satisfy some cogenerating(resp.,generating)conditions.Applications of the results are given:we show that tilting(resp.,cotilting)subcategories defined here unify many previous works about tilting modules(subcategories)in module categories of Artin algebras and in abelian categories admitting a cotorsion triples;we also show that the results work for the triangulated categories with a proper class of triangles introduced by A.Beligiannis. 相似文献
12.
We know that in Ringel–Hall algebra of Dynkin type, the set of all skew commutator relations between the iso-classes of indecomposable modules forms a minimal Gr?bner–Shirshov basis,and the corresponding irreducible elements forms a PBW type basis of the Ringel–Hall algebra. We aim to generalize this result to the derived Hall algebra DH(A_n) of type A_n. First, we compute all skew commutator relations between the iso-classes of indecomposable objects in the bounded derived category D~b(A_n) using the Auslander–Reiten quiver of D~b(A_n), and then we prove that all possible compositions between these skew commutator relations are trivial. As an application, we give a PBW type basis of DH(A_n). 相似文献
13.
14.
In continuation of our earlier work [2] we describe the indecomposable representations and the Auslander-Reiten quivers of
a family of vector space categories playing an important role in the study of domestic finite dimensional algebras over an
algebraically closed field. The main results of the paper are applied in our paper [3] where we exhibit a wide class of almost
sincere domestic simply connected algebras of arbitrary large finite global dimensions and describe their Auslander-Reiten
quivers. 相似文献
15.
When the base connected cochain DG algebra is cohomologically bounded, it is proved that the difference between the amplitude
of a compact DG module and that of the DG algebra is just the projective dimension of that module. This yields the unboundedness
of the cohomology of non-trivial regular DG algebras.
When A is a regular DG algebra such that H(A) is a Koszul graded algebra, H(A) is proved to have the finite global dimension. And we give an example to illustrate that the global dimension of H(A) may be infinite, if the condition that H(A) is Koszul is weakened to the condition that A is a Koszul DG algebra. For a general regular DG algebra A, we give some equivalent conditions for the Gorensteiness.
For a finite connected DG algebra A, we prove that Dc(A) and Dc(A
op) admit Auslander-Reiten triangles if and only if A and A
op are Gorenstein DG algebras. When A is a non-trivial regular DG algebra such that H(A) is locally finite, Dc(A) does not admit Auslander-Reiten triangles. We turn to study the existence of Auslander-Reiten triangles in Dlfb(A) and Dlfb (A
op) instead, when A is a regular DG algebra.
This work was supported by the National Natural Science Foundation of China (Grant No. 10731070) and the Doctorate Foundation
of Ministry of Education of China (Grant No. 20060246003) 相似文献
16.
In the paper, we introduce a wide class of domestic finite dimensional algebras over an algebraically closed field which are
obtained from the hereditary algebras of Euclidean type
, n≥1, by iterated one-point extensions by two-ray modules. We prove that these algebras are domestic and their Auslander-Reiten
quivers admit infinitely many nonperiodic connected components with infinitely many orbits with respect to the action of the
Auslander-Reiten translation. Moreover, we exhibit a wide class of almost sincere domestic simply connected algebras of large
global dimensions. 相似文献
17.
Auslander-Reiten triangles and quivers are introduced into algebraic
topology.
It is proved that the existence of Auslander-Reiten triangles characterizes Poincaré
duality spaces, and that the Auslander-Reiten quiver is a weak
homotopy invariant.
The theory is applied to spheres whose Auslander-Reiten triangles and quivers are
computed. The Auslander-Reiten quiver over the $d$-dimensional sphere turns out to
consist of $d-1$ copies of ${\mathbb Z} A_{\infty}$. Hence the quiver is a
sufficiently sensitive invariant to tell spheres of different
dimension apart. 相似文献
18.
For finite semidistributive lattices the map κ gives a bijection between the sets of completely join-irreducible elements and completely meet-irreducible elements.Here we study the κ-map in the context of torsion classes. It is well-known that the lattice of torsion classes for an artin algebra is semidistributive, but in general it is far from finite. We show the κ-map is well-defined on the set of completely join-irreducible elements, even when the lattice of torsion classes is infinite. We then extend κ to a map on torsion classes which have canonical join representations given by the special torsion classes associated to the minimal extending modules introduced by the first and third authors and A. Carroll in 2019.For hereditary algebras, we show that the extended κ-map on torsion classes is essentially the same as Ringel's ?-map on wide subcategories. Also in the hereditary case, we relate the square of κ to the Auslander-Reiten translation. 相似文献
19.
Sarah Scherotzke 《Journal of Pure and Applied Algebra》2011,215(3):232-241
We analyze Auslander-Reiten components for the bounded derived category of a finite-dimensional algebra. We classify derived categories whose Auslander-Reiten quiver has either a finite stable component or a stable component with finite Dynkin tree class or a bounded stable component. Their Auslander-Reiten quivers are determined. We also determine components that contain shift periodic complexes. 相似文献