共查询到20条相似文献,搜索用时 31 毫秒
1.
《Journal of Pure and Applied Algebra》2022,226(4):106862
We investigate how to characterize subcategories of abelian categories in terms of intrinsic axioms. In particular, we find axioms which characterize generating cogenerating functorially finite subcategories, precluster tilting subcategories, and cluster tilting subcategories of abelian categories. As a consequence we prove that any d-abelian category is equivalent to a d-cluster tilting subcategory of an abelian category, without any assumption on the categories being projectively generated. 相似文献
2.
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
3.
Changjian Fu 《代数通讯》2013,41(7):2410-2418
We show that a tilting module over the endomorphism algebra of a cluster-tilting object in a 2-Calabi–Yau triangulated category lifts to a cluster-tilting object in this 2-Calabi–Yau triangulated category. This generalizes a recent work of Smith for cluster categories. 相似文献
4.
Aslak Bakke Buan Robert J. Marsh Idun Reiten 《Transactions of the American Mathematical Society》2007,359(1):323-332
We introduce a new class of algebras, which we call cluster-tilted. They are by definition the endomorphism algebras of tilting objects in a cluster category. We show that their representation theory is very close to the representation theory of hereditary algebras. As an application of this, we prove a generalised version of so-called APR-tilting.
5.
Let C be a connected Noetherian hereditary Abelian category with a Serre functor over an algebraically closed field k, with finite-dimensional homomorphism and extension spaces. Using the classification of such categories from our 1999 preprint, we prove that if C has some object of infinite length, then the Grothendieck group of C is finitely generated if and only if C has a tilting object. 相似文献
6.
本文研究了2-Calabi-Yau三角范畴上的2-Calabi-Yau tilted代数的almost complete tilting模.我们利用2-Calabi-Yau三角范畴上的交换关系给出了2-Calabi-Yau tilted代数的almost complete tilting模有两个(Bongartz)补的一系列充分必要条件. 相似文献
7.
Using the cluster tilting theory,we investigate the tilting objects in the stable category of vector bundles on a weighted projective line of weight type(2,2,2,2).More precisely,a tilting object consisting of rank-two bundles is constructed via the cluster tilting mutation.Moreover,the cluster tilting approach also provides a new method to classify the endomorphism algebras of the tilting objects in the category of coherent sheaves and the associated bounded derived category. 相似文献
8.
Let H be a finite-dimensional hereditary algebra over an algebraically closed field k and CFm be the repetitive cluster category of H with m ≥ 1. We investigate the properties of cluster tilting objects in CFm and the structure of repetitive cluster-tilted algebras. Moreover, we generalize Theorem 4.2 in [12] (Buan A, Marsh R, Reiten I. Cluster-tilted algebra, Trans. Amer. Math. Soc., 359(1)(2007), 323-332.) to the situation of CFm, and prove that the tilting graph KCFm of CFm is connected. 相似文献
9.
Let (C,E,s) be an extriangulated category with a proper class ξ of E-triangles.We study complete cohomology of objects in (C,E,s) by applying ξ-projective resolutions and ξ-injective coresolutions constructed in (C,E,s).Vanishing of complete cohomology detects objects with finite ξ-projective dimension and finite ξ-injective dimension.As a consequence,we obtain some criteria for the validity of the Wakamatsu tilting conjecture and give a necessary and sufficient condition for a virtually Gorenstein algebra to be Gorenstein.Moreover,we give a general technique for computing complete cohomology of objects with finite ξ-Gprojective dimension.As an application,the relations between ξ-projective dimension and ξ-Gprojective dimension for objects in (C,E,s) are given. 相似文献
10.
Cyclic posets are generalizations of cyclically ordered sets. In this article, we show that any cyclic poset gives rise to a Frobenius category over any discrete valuation ring R. The stable category of a Frobenius category is always triangulated and has a cluster structure in many cases. The continuous cluster categories of [14], the infinity-gon of [12], and the m-cluster category of type A ∞ (m ≥ 3) [13] are examples of this construction as well as some new examples such as the cluster category of ?2. An extension of this construction and further examples are given in [16]. 相似文献
11.
陈娟 《数学的实践与认识》2012,(1):188-194
κ-线性范畴是有限维κ-代数的自然推广.对应于双扩张代数,定义了κ-线性双扩张范畴■,并且证明了■Mod等价于四元组范畴■,推广了双扩张代数的模范畴理论. 相似文献
12.
13.
The trivial extensions of a quasi-abelian category by means of a fully exact endofunctor are again quasi-abelian. Using the
one-to-one correspondence between quasi-abelian categories and tiltings, it is shown that the trivial extension of a quasi-abelian
category corresponds to a trivial extension of the associated tilting. As an application, a criterion for tilting modules
over an arbitrary ring R to be liftable to a tilting module over a trivial extension ring
R\ltimes M{R\ltimes M} is given. 相似文献
14.
Let A be a finite dimensional algebra, the Bongartz lemma for classic tilting modules says that any partial tilting module is a direct summand of a tilting module. In this paper, we prove that a Bongartz-type lemma for silting complexes in the bounded derived category $$D^b(A)$$ holds if A is a hereditary algebra. 相似文献
15.
This paper gives the relationships among partial tilting objects (tilting objects) of categories of graded left A-modules of type G, left A-modules, left Ae-modules and A#-modules, and then proves that for graded partial tilting modules, there exist the Bongartz complements in the category of graded A-modules. 相似文献
16.
Let 𝒞 be an additive category. Denote by End(𝒞) the endomorphism category of 𝒞, i.e., the objects in End(𝒞) are pairs (C,c) with C∈𝒞,c∈End𝒞(C), and a morphism f:(C,c)→(D,d) is a morphism f∈Hom𝒞(C,D) satisfying fc?=?df. This paper is devoted to an approach of the general theory of the endomorphism category of an arbitrary additive category. It is proved that the endomorphism category of an abelian category is again abelian with an induced structure without nontrivial projective or injective objects. Furthermore, the endomorphism category of any nontrivial abelian category is nonsemisimple and of infinite representation type. As an application, we show that two unital rings are Morita equivalent if and only if the endomorphism categories of their module categories are equivalent. 相似文献
17.
XiaoJuan Zhao 《中国科学 数学(英文版)》2014,57(11):2329-2334
Let A and B be finite-dimensional algebras over a field k of finite global dimension. Using some results of Gorsky in “Semi-derived Hall algebras and tilting invariance of Bridgeland-Hall algebras”, we prove that if A and B are derived equivalent, then the corresponding m-periodic derived categories are triangulated equivalent. 相似文献
18.
Yu-Han Liu 《代数通讯》2013,41(8):3013-3031
We compute Balmer's prime spectrum for the derived category of quiver representations for a finite ordered quiver with the vertex-wise tensor product and show that it does not recover the quiver. We then associate an algebra to every k-linear triangulated tensor category and show that the path algebra can be recovered in this way. 相似文献
19.
This note investigates the modules over the endomorphism algebras of maximal rigid objects in 2-Calabi-Yau triangulated categories. We study the possible complements for almost complete tilting modules. Combining with Happel's theorem, we show that the possible exchange sequences for tilting modules over such algebras are induced by the exchange triangles for maximal rigid objects in the corresponding 2-Calabi-Yau triangulated categories. For the modules of infinite projective dimension, we generalize a recent result by Beaudet–Brüstle–Todorov for cluster-tilted algebras. 相似文献
20.
Hiroki Abe 《代数通讯》2017,45(9):3917-3928
We construct a diagram between the endomorphism algebra of a two-term projective module complex over a self-injective algebra and the endomorphism algebras of its homology groups and apply the diagram to the tilting theory of self-injective algebras. We give an example of recovering the endomorphism algebra of a two-term tilting complex over a self-injective algebra from the endomorphism algebras of its homology groups with some additional structures which appear in the diagram. 相似文献