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1.
设A是有限域上的A11型的遗传代数,YE(A)T和C(A)分别表示A的Ringel-Hall代数和合成代数,该文证明了C(A)=Y,Y.Y,其中Y和,K分别表示由预投射模和预内射模生成的子代数,Y是由C(A)中的正则元素生成的代数。  相似文献   

2.
张跃辉  利煜 《工科数学》2000,16(3):9-11
本文给出了树型代数的拟遗传序数的精确上界以及单生成元的树型代数的拟遗传序列的精确下界及其算法,并由此得到一个新的组合公式。  相似文献   

3.
本文给出了树型代数的拟遗传序数的精确上界以及单生成元的树型代数的拟遗传序数的精确下界及其算法 ,并由此得到一个新的组合公式 .  相似文献   

4.
本文讨论双生成元$A_n$型代数的拟遗传序的性质,给出了该类代数的单模序是拟遗传序的充分必要条件,并利用组合技巧得出了该类代数拟遗传序的数目.  相似文献   

5.
张英伯  肖杰 《数学进展》1993,22(6):481-501
代数表示论是本世纪七十年代初兴起的代数学的一个新的分支。它的基本内容是研究一个Artin代数上的模范畴。由于各国代数学家的共同努力,这一理论于最近二十年代有了异常迅猛的发展并逐步趋于完善。本文介绍了代数表示论的理论基础;几乎可裂序列;箭图和赋值箭图的表示;Coxeter函子;AR-箭图的覆盖及代数的Galois覆盖。并简单介绍了在代数表示论中普遍应用的工具:Tilt理论,以及著名的Dpozg定理证  相似文献   

6.
代数正规类中的遗传根与强半单根   总被引:5,自引:0,他引:5  
Puczylowski建立了一般代数对象类的根理论.本文在代数正规类中,用格论方法刻划一般遗传根和强半单根类,探究它们的一些性质,推广了已知各类代数系统的某些根论研究.  相似文献   

7.
设 $\Lambda$ 是域$k$上的有限维代数. 则 $\Lambda$的低阶 Hochschild上同调群在有限维代数的表示理论中扮演着重要的角色. 该文得到了 $l$ -遗传代数的一阶和二阶Hochschild 上同调群的维数方程.  相似文献   

8.
朱彬 《数学年刊A辑》2001,22(2):135-140
本文考虑拟遗传代数上的△一好模范畴f(△)的Grothendieck群的生成关系.利用它刻划了f(△)-有限的拟遗传代数和表示有限的直向代数.  相似文献   

9.
本文利用exactBorel子代数刻划了遗传代数,给出了basic拟遗传代数的主子代数是exactBorel子代数的充分必要条件.  相似文献   

10.
本文考虑拟遗传代数上的△一好模范畴F(△)的 Grothendieck群的生成关系.利用它刻划了F(△)-有限的拟遗传代数和表示有限的直向代数.  相似文献   

11.
In order to study the representation theory of Lie algebras and algebraic groups, Cline, Parshall and Scott put forward the notion of abstract Kazhdan-Lusztig theory for quasihereditary algebras. Assume that a quasi-hereditary algebra B has the vertex set Q0 = {1,..., n} such that HomB(P(i), P(j)) = 0 for i 〉 j. In this paper, it is shown that if the quasi-hereditary algebra B has a Kazhdan-Lusztig theory relative to a length function l, then its dual extension algebra A = .A(B) has also the Kazhdan-Lusztig theory relative to the length function l.  相似文献   

12.
Quasi-hereditary algebras can be viewed as a Lie theory approach to the theory of finite dimensional algebras. Motivated by the existence of certain nice bases for representations of semisimple Lie algebras and algebraic groups, we will construct in this paper nice bases for (split) quasi-hereditary algebras and characterize them using these bases. We first introduce the notion of a standardly based algebra, which is a generalized version of a cellular algebra introduced by Graham and Lehrer, and discuss their representation theory. The main result is that an algebra over a commutative local noetherian ring with finite rank is split quasi-hereditary if and only if it is standardly full-based. As an application, we will give an elementary proof of the fact that split symmetric algebras are not quasi-hereditary unless they are semisimple. Finally, some relations between standardly based algebras and cellular algebras are also discussed.  相似文献   

13.
A Construction of Characteristic Tilting Modules   总被引:4,自引:0,他引:4  
Associated with each finite directed quiver Q is a quasi-hereditary algebra, the so-called twisted double of the path algebra kQ. Characteristic tilting modules over this class of quasi-hereditary algebras are constructed. Their endomorphism algebras are explicitly described. It turns out that this class of quasi-hereditary algebras is closed under taking the Ringel dual. Received November 15, 2000, Accepted March 5, 2001  相似文献   

14.
The paper is a continuation of the authors' study of quasi-hereditary algebras whose Yoneda extension algebras (homological duals) are quasi-hereditary. The so-called standard Koszul quasi-hereditary algebras, presented in this paper, have the property that their extension algebras are always quasi-hereditary. In the natural setting of graded Koszul algebras, the converse also holds: if the extension algebra of a graded Koszul quasi-hereditary algebra is quasi-hereditary, then the algebra must be standard Koszul. This implies that the class of graded standard Koszul quasi-hereditary algebras is closed with respect to homological duality. Another immediate consequence is the fact that all algebras corresponding to the blocks of the category O are standard Koszul.  相似文献   

15.
Weyl代数研究简介   总被引:2,自引:0,他引:2  
李会师 《数学进展》1998,27(2):103-121
本文简要综述Weyl代数诞生70余年来的一系列重要研究成果。  相似文献   

16.
素特征李代数概述   总被引:1,自引:0,他引:1  
林磊 《数学进展》1995,24(1):28-38
近20年来,国内外在素特征李代数的研究中取得了许多突破性的进展,本文是近年来国内外在这一领域的研究成果的一个综述,第一部分对Cartan型李代数的定义以及主要结构的回顾,然后,重点介绍了两个重的分类定理,即,素特征域上的有限维局限单李代数的分类定理以及素特征域上的有际维单李代的分类定理。由于后一分类是一前一分类的基础上完成的,所以,本文对第一个分类定理的证明作了一个简单的介绍,在第三部分中,对素特  相似文献   

17.
We give an alternative proof to the fact that, if the square of the infinite radical of the module category of an Artin algebra is equal to zero, then the algebra is of finite type by making use of the theory of postprojective and preinjective partitions. Further, we use this new approach in order to get a characterization of finite subcategories of Δ-good modules of a quasi-hereditary algebra in terms of depth of morphisms similar to a recently obtained characterization of Artin algebras of finite type.  相似文献   

18.
We study Auslander's representation dimension of Artin algebras, which is by definition the minimal projective dimension of coherent functors on modules which are both generators and cogenerators. We show the following statements: (1) if an Artin algebra A is stably hereditary, then the representation dimension of A is at most 3. (2) If two Artin algebras are stably equivalent of Morita type, then they have the same representation dimension. Particularly, if two self-injective algebras are derived equivalent, then they have the same representation dimension. (3) Any incidence algebra of a finite partially ordered set over a field has finite representation dimension. Moreover, we use results on quasi-hereditary algebras to show that (4) the Auslander algebra of a Nakayama algebra has finite representation dimension.  相似文献   

19.
A realization by linear vector fields is constructed for any Lie algebra which admits a biorthogonal system and for its any suitable representation. The embedding into Lie algebras of linear vector fields is in analogue to the classical Jordan—Schwinger map. A number of examples of such Lie algebras of linear vector fields is computed. In particular, we obtain examples of the twisted Heisenberg-Virasoro Lie algebra and the Schrödinger-Virasoro Lie algebras among others. More generally, we construct an embedding of an arbitrary locally convex topological algebra into the Cuntz algebra.  相似文献   

20.
In this paper, we study the Lie algebras in which every subspace is its subalgebra (denoted by HB Lie algebras). We get that a nonabelian Lie algebra is an HB Lie algebra if and only if it is isomorphic to g+Cidg, where g is an abelian Lie algebra. Moreover we show that the derivation algebra and the holomorph of a nonabelian HB Lie algebra are complete.  相似文献   

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