共查询到20条相似文献,搜索用时 31 毫秒
1.
We generalize derived equivalences for triangular matrix rings induced by a certain type of classical tilting module introduced by Auslander, Platzeck and Reiten to generalize reflection functors in the representation theory of quivers due to Bernstein, Gelfand and Ponomarev. 相似文献
2.
Houjun Zhang 《代数通讯》2020,48(2):467-483
AbstractIn this article, we investigate the Gorenstein global dimension with respect to the recollements of abelian categories. With the invariants spli and silp of the categories, we give some upper bounds of Gorenstein global dimensions of the categories involved in a recollement of abelian categories. We apply our results to some rings and artin algebras, especially to the triangular matrix artin algebras. 相似文献
3.
Yongyun Qin 《代数通讯》2018,46(1):356-367
We investigate the behavior of the homological dimensions under recollements of derived categories of algebras. In particular, we establish a series of new bounds among the self-injective dimensions or ?-dimensions of the algebras linked by recollements of derived module categories. 相似文献
4.
Bimodules over triangular Nakayama algebras that give stable equivalences of Morita type are studied here. As a consequence
one obtains that every stable equivalence of Morita type between triangular Nakayama algebras is a Morita equivalence. 相似文献
5.
We study the problem of lifting and restricting TTF triples (equivalently, recollement data) for a certain wide type of triangulated
categories. This, together with the parametrizations of TTF triples given in Nicolás and Saorín (Parametrizing recollement
data for triangulated categories. To appear in J. Algebra), allows us to show that many well-known recollements of right bounded
derived categories of algebras are restrictions of recollements in the unbounded level, and leads to criteria to detect recollements
of general right bounded derived categories. In particular, we give in Theorem 1 necessary and sufficient conditions for a
right bounded derived category of a differential graded (=dg) category to be a recollement of right bounded derived categories of dg categories.
Theorem 2 considers the case of dg categories with cohomology concentrated in non-negative degrees. In Theorem 3 we consider
the particular case in which those dg categories are just ordinary algebras. 相似文献
6.
The aim of this article is to study some invariants of associative algebras under stable equivalences of Morita type.First of all,we show that,if two finite-dimensional selfinjective k-algebras are sta... 相似文献
7.
8.
Shengyong Pan 《Algebras and Representation Theory》2014,17(3):885-903
In this paper, we introduce a class of algebras called Φ-Cohen–Macaulay Auslander–Yoneda algebras with Φ an admissible set of ?, and construct derived equivalences between these Φ-Cohen–Macaulay Auslander–Yoneda algebras from a given derived equivalence. 相似文献
9.
We apply tilting theory over preprojective algebras Λ to the study of moduli spaces of Λ-modules. We define the categories of semistable modules and give equivalences, so-called reflection functors, between them by using tilting modules over Λ. Moreover we prove that the equivalence induces an isomorphism of K-schemes between moduli spaces. In particular, we study the case when the moduli spaces are related to Kleinian singularities, and generalize some results of Crawley-Boevey (Am J Math 122:1027–1037, 2000). 相似文献
10.
Gorenstein derived categories are defined, and the relation with the usual derived categories is given. The bounded Gorenstein derived categories of Gorenstein rings and of finite-dimensional algebras are explicitly described via the homotopy categories of Gorenstein-projective modules, and some applications are obtained. Gorenstein derived equivalences between CM-finite Gorenstein algebras are discussed. 相似文献
11.
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
12.
Characteristic tilting modules and Ringel duals 总被引:6,自引:0,他引:6
XI Changchang 《中国科学A辑(英文版)》2000,43(11):1121-1130
The characteristic tilting modules of quasi-hereditary algebras which are dual extensions of directed monomial algebras are
explicitly constructed; and it is shown that the Ringel dual of the dual extension of an arbitrary hereditary algebra has
triangular decomposition and bipartite quiver. 相似文献
13.
Recollements and tilting objects 总被引:1,自引:0,他引:1
We study connections between recollements of the derived category D(Mod R) of a ring R and tilting theory. We first provide constructions of tilting objects from given recollements, recovering several different results from the literature. Secondly, we show how to construct a recollement from a tilting module of projective dimension one. By Nicolás and Saorín (2009) [31], every recollement of D(Mod R) is associated to a differential graded homological epimorphism λ:R→S. We will focus on the case where λ is a homological ring epimorphism or even a universal localization. Our results will be employed in a forthcoming paper in order to investigate stratifications of D(Mod R). 相似文献
14.
For any positive integer N,we clearly describe all finite-dimensional algebras A such that the upper triangular matrix algebras TN(A) are piecewise hereditary.Consequently,we describe all finite-dimensional algebras A such that their derived categories of N-complexes are triangulated equivalent to derived categories of hereditary abelian categories,and we describe the tensor algebras A (×) K[X]/(XN) for which their singularity categories are triangulated orbit categories of the derived categories of hereditary abelian categories. 相似文献
15.
Jorge Vitória 《Journal of Algebra》2009,321(3):816-828
For a quiver with potential, Derksen, Weyman and Zelevinsky defined in [H. Derksen, J. Weyman, A. Zelevinsky, Quivers with potentials and their representations I: Mutations, arXiv: 0704.0649v2 [math.RA]] a combinatorial transformation, mutations. Mukhopadhyay and Ray, on the other hand, tell us how to compute Seiberg dual quivers for some quivers with potentials through a tilting procedure, thus obtaining derived equivalent algebras. In this text, we compare mutations with the concept of Seiberg duality given by [S. Mukhopadhyay, K. Ray, Seiberg duality as derived equivalence for some quiver gauge theories, arXiv: hep-th/0309191v2], concluding that for a certain class of potentials (the good ones) mutations coincide with Seiberg duality, therefore giving derived equivalences. 相似文献
16.
Sheng Yong Pan 《数学学报(英文版)》2016,32(4):439-456
Let A be a small abelian category. For a closed subbifunctor F of ExtA1(-,-), Buan has generalized the construction of Verdier's quotient category to get a relative derived category, where he localized with respect to F-acyclic complexes. In this paper, the homological properties of relative derived categories are discussed, and the relation with derived categories is given. For Artin algebras, using relative derived categories, we give a relative version on derived equivalences induced by F-tilting complexes. We discuss the relationships between relative homological dimensions and relative derived equivalences. 相似文献
17.
Jiaqun Wei 《Mathematische Zeitschrift》2012,272(1-2):431-441
We studied the properties of tilting complexes and proved that derived equivalences preserve the validity of the Auslander–Reiten conjecture. 相似文献
18.
Lucas David-Roesler 《Algebras and Representation Theory》2014,17(1):1-30
We determine some of the derived equivalences of a class of gentle algebras called surface algebras. These algebras are constructed from an unpunctured Riemann surface of genus 0 with boundary and marked points by introducing cuts in internal triangles of an arbitrary triangulation of the surface. In particular, we fix a triangulation of a surface and determine when different cuts produce derived equivalent algebras. 相似文献
19.
Ming Lu 《Algebras and Representation Theory》2016,19(6):1257-1295
We define a class of finite-dimensional Jacobian algebras, which are called (simple) polygon-tree algebras, as a generalization of cluster-tilted algebras of type \(\mathbb {D}\). They are 2-CY-tilted algebras. Using a suitable process of mutations of quivers with potential (which are also BB-mutations) inducing derived equivalences, and one-pointed (co)extensions which preserve singularity equivalences, we find a connected selfinjective Nakayama algebra whose stable category is equivalent to the singularity category of a simple polygon-tree algebra. Furthermore, we also give a classification of algebras of this kind up to representation type. 相似文献
20.
We introduce a notion of Gorenstein algebras of codimension c and demonstrate that Serre duality theory plays an essential role in the theory of derived equivalences for Gorenstein algebras. 相似文献