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1.
X.-F. Mao 《代数通讯》2013,41(8):3050-3072
In this article, we study various homological invariants of differential graded (DG for short) modules over a connected DG algebra following Frankild–Jørgensen. Two different versions of homological dimensions (resolutional and functorial) are defined. In some cases, they are proved to be simply the bound of the cohomology of the DG module. Some homological identities, such as Auslander–Buchsbaum formula and Bass formula, are proved for compact DG modules over a connected DG algebra.  相似文献   

2.
X.-F. Mao  Q.-S. Wu 《代数通讯》2013,41(5):1536-1562
As the definition of free class of differential modules over a commutative ring in [1 Avramov , L. L. , Buchweitz , R.-O. , Iyengar , S. ( 2007 ). Class and rank of differential modules . Invent. Math. 169 : 135 .[Crossref], [Web of Science ®] [Google Scholar]], we define DG free class for semifree DG modules over an Adams connected DG algebra A. For any DG A-modules M, we define its cone length as the least DG free classes of all semifree resolutions of M. The cone length of a DG A-module plays a similar role as projective dimension of a module over a ring does in homological ring theory. The left (resp., right) global dimension of an Adams connected DG algebra A is defined as the supremum of the set of cone lengths of all DG A-modules (resp., A op -modules). It is proved that the definition is a generalization of that of graded algebras. Some relations between the global dimension of H(A) and the left (resp. right) global dimension of A are discovered. When A is homologically smooth, we prove that the left (right) global dimension of A is finite and the dimension of D(A) and D c (A) are not bigger than the DG free class of a minimal semifree resolution X of the DG A e -module A.  相似文献   

3.
陈健敏  林亚南 《数学学报》2006,49(2):347-352
设A是由箭图Q和关系I所确定的代数,D(A)是代数A的对偶扩张代数, 对应的箭图Q*和关系I*由Q和I决定.本文证明:带关系箭图(Q*,I*)的自同构由带关系箭图(Q,I)的自同构决定;D(A)的Frobenius态射由A的Frobenius态射完全决定;代数D(A)的固定点代数同构于相应的代数A的固定点代数与A°P的固定点代数的张量积,特别地,当Q为单的箭图时,代数D(A)的固定点代数同构于代数A的固定点代数的对偶扩张代数.  相似文献   

4.
In the present paper the properties of morphisms in effect algebras are discussed. The conditions for the morphisms in effect algebras to be join-preservation and meet-preservation are given. From the categorical point of view, some properties of ideals, filters and congruence relations under morphisms are obtained.  相似文献   

5.
6.
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   

7.
一类特殊的Koszul Calabi-Yau DG代数   总被引:1,自引:0,他引:1  
毛雪峰  何继位 《数学学报》2017,60(3):475-504
假设一个连通上链DG代数A的基分次代数A~#或者同调分次代数H(A)是由一次元素x,y生成的代数kx,y/(xy+yx).本文证明A是Koszul Calabi-Yau DG代数.  相似文献   

8.
本文给出了Z_n分次代数A的Hochschild上同调群的定义,对低阶Hochschild上同调群进行了刻画.利用第一阶Hochschild上同调群给出了Z_n分次代数为分次可分代数的充要条件,证明了第二阶Hochschild上同调群的零次分支与A的Hochschild扩张之间的一一对应关系.  相似文献   

9.
The algebras of derivations of naturally graded Leibniz algebras are described. The existence of characteristically nilpotent Leibniz algebras in any dimension greater than 4 is proved.__________Translated from Matematicheskie Zametki, vol. 77, no. 5, 2005, pp. 733–742.Original Russian Text Copyright ©2005 by B. A. Omirov.  相似文献   

10.
毛雪峰  谢建峰 《数学学报》2018,61(5):715-728
本文给出了有关同调光滑连通上链微分分次(简称DG)代数的两个重要结论.具体地说,当A是同调光滑连通上链DG代数且其同调分次代数H(A)是诺特分次代数时,证明D_(fg)(A)中的任意Koszul DG A-模都是紧致的.另外,当A是Kozul连通上链DG代数且其同调分次代数H(A)是有平衡对偶复形的诺特分次代数时,证明A的同调光滑性质等价于D_(fg)(A)=D~c(A).  相似文献   

11.
We provide examples of finitely generated noetherian PI algebras for which there is no finite dimensional filtration with a noetherian associated graded ring; thus we answer negatively a question of Lorenz (1988).

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12.
本文的目的 是定义Hopf二重Ore扩张,讨论这种扩张的基本性质并研究Hopf代数的分次与Hopf二重Ore扩张之间的关系.作者还研究了连通分次Hopf代数的结构及其Hopf二重Ore扩张的同调性质.  相似文献   

13.
Malihe Yousofzadeh 《代数通讯》2013,41(12):4277-4302
We introduce a new class of possibly infinite dimensional Lie algebras and study their structural properties. Examples of this new class of Lie algebras are finite dimensional simple Lie algebras containing a nonzero split torus, affine and extended affine Lie algebras. Our results generalize well-known properties of these examples.  相似文献   

14.
In this article, we study an important subalgebra of the tensor product partition algebra P k (x)? P k (y), denoted by P k (x, y) and called “Class Partition Algebra.” We show that the algebra P k (n, m) is the centralizer algebra of the wreath product S m ? S n . Furthermore, the algebra P k (x, y) and the tensor product partition algebra P k (x)? P k (y) are subalgebras of the G-colored partition algebra P k (x;G) and G-vertex colored partition algebra P k (x, G) respectively, for every group G with |G|=y ≥ 2k.  相似文献   

15.
We introduce the category of t-fold modules which is a full subcategory of graded modules over a graded algebra. We show that this subcategory and hence the subcategory of t-Koszul modules are both closed under extensions and cokernels of monomorphisms. We study the one-point extension algebras, and a necessary and sufficient condition for such an algebra to be t-Koszul is given. We also consider the conditions such that the category of t-Koszul modules and the category of quadratic modules coincide.  相似文献   

16.
Katsutoshi Amano 《代数通讯》2013,41(5):1811-1823
In a previous article (Amano and Masuoka, 2005 Amano , K. , Masuoka , A. ( 2005 ). Picard–Vessiot extensions of Artinian simple module algebras . J. Algebra 285 : 743767 . [CSA] [Crossref], [Web of Science ®] [Google Scholar]), the author and Masuoka developed a Picard–Vessiot theory for module algebras over a cocommutative pointed smooth Hopf algebra D. By using the notion of Artinian simple (AS)D-module algebras, it generalizes and unifies the standard Picard–Vessiot theories for linear differential and difference equations. The purpose of this article is to define the notion of Liouville extensions of AS D-module algebras and to characterize the corresponding Picard–Vessiot group schemes.  相似文献   

17.
The concept of Koszul differential graded (DG for short) algebra is introduced in [8]. Let A be a Koszul DG algebra. If the Ext-algebra of A is finite-dimensional, i.e., the trivial module Ak is a compact object in the derived category of DG A-modules, then it is shown in [8] that A has many nice properties. However, if the Ext-algebra is infinite-dimensional, little is known about A. As shown in [15] (see also Proposition 2.2), Ak is not compact if H(A) is finite-dimensional. In this paper, it is proved that the Koszul duality theorem also holds when H(A) is finite-dimensional by using Foxby duality. A DG version of the BGG correspondence is deduced from the Koszul duality theorem.  相似文献   

18.
19.
Kristen A. Beck 《代数通讯》2013,41(4):1640-1653
Let A be a differential graded (DG) algebra with a trivial differential over a commutative unital ring. This paper investigates the image of the totaling functor, defined from the category of complexes of graded A-modules to the category of DG A-modules. Specifically, we exhibit a special class of semifree DG A-modules which can always be expressed as the totaling of some complex of graded free A-modules. As a corollary, we also provide results concerning the image of the totaling functor when A is a polynomial ring over a field.  相似文献   

20.
马盈仓  李会师 《数学进展》2003,32(3):327-333
本文给出K—代数A上一种较为广泛的阶法子,在此滤子下运用Groebner基理论,给出了A和两个分次代数grC(A)与(A^~)的关系。  相似文献   

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