拟遗传代数的Exact Borel子代数与主子代数

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．     

双生成元$A_n$型拟遗传代数的拟遗传序

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.     

树型代数拟遗传序的组合公式及其算法

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 .     

双模问题rad~t(-,-)与拟遗传代数

设 Ｂ是 Ｋｒｕｌｌ－ｓｃｈｍｉｄｔ范畴 Ｋ上的一个上三角双模，Ｂｒｕｓｔｌｅ和 Ｈｉｌｌｅ证明了Ｂ的矩阵范畴ｍａｔＢ的投射生成子Ｐ的自同态代数的反代数Ａ是拟遗传代数，而且代数Ａ的△－好模范畴与ｍａｔＢ等价．本文把这些结果推广到由Ｃｒａｗｌｅｙ-Ｂｏｅｖｅｙ给出的具有非零导子的双模上，并在此基础上着重讨论了遗传代数 的投射模范畴Ｐｒｏｊ上的双模ｒａｄｔ（－，－），刻画了它所对应的拟遗传代数的Ｇａｂｒｉｅｌ箭图与关系，以及它们的特征模和Ｒｉｎｇｅｌ对偶．     

树型代数拟遗传序的组合公式及其算法

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。     

代数表示论的某些新进展

代数表示理论是代数学的一个新的重要分支，在近二十五年的时间里，这一理论有很大的发展，关于代数表示的基础理论的介绍可参见文献（１０１），本文主要从Ｈａｌｌ代数和拟遗传代数两个方面介绍代数表示论的一些最新进展，第一章给出了Ｈａｌｌ代数的基本理论及其方法，并且着重指出了利用这一理论和方法通过代数表示论去实现Ｋａｃ－Ｍｏｏｄｙ李代数及相应的量子包络代数，第二章介绍了拟遗传代数及其表示理论，以及这一理论与复     

拟遗传代数的Grothendieck群的生成关系

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.     

有限复杂度的Koszul代数

首先给出了Koszul代数的张量积的复杂度,然后研究了Koszul遗传代数上的Koszul单列模,并证明了Koszul遗传代数上的Koszul模M的Koszul合成列在同构意义下是唯一的.     

遗传群体的代数系统

根据生物遗传的内在规律,在多基因座配子中构造了一类运算,阐明了生物遗传具有交换的R-代数的数学结构,从而使遗传问题可用代数方法解决.文中利用这种代数所得到的因子频率定理,具有比Hardy-Weinberg平衡定律更为广泛的意义.同时,作为这种代数应用的例子,讨论了在连锁条件下群体基因型频率的计算问题,得到了一系列有意义的结果.     

拟遗传代数的Grothendieck群的生成关系

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．     

Algebras, hyperalgebras, nonassociative bialgebras and loops

Sabinin algebras are a broad generalization of Lie algebras that include Lie, Malcev and Bol algebras as very particular examples. We present a construction of a universal enveloping algebra for Sabinin algebras, and the corresponding Poincaré-Birkhoff-Witt Theorem. A nonassociative counterpart of Hopf algebras is also introduced and a version of the Milnor-Moore Theorem is proved. Loop algebras and universal enveloping algebras of Sabinin algebras are natural examples of these nonassociative Hopf algebras. Identities of loops move to identities of nonassociative Hopf algebras by a linearizing process. In this way, nonassociative algebras and Hopf algebras interlace smoothly.     

Composition Algebras with Large Derivation Algebras

The finite dimensional flexible composition algebras include the Hurwitz algebras (composition algebras with unit element), but also other interesting classes of algebras: the para-Hurwitz and the Okubo algebras. The above mentioned algebras present many symmetries, and this is reflected in their large derivation algebras. In the present paper we study the opposite question: What can be said about the composition algebras if we have some information about their derivation algebras? Our main result is the classification of all the composition algebras with such large derivation algebras.     

Schur algebras of Brauer algebras I

Schur algebras of Brauer algebras are defined as endomorphism algebras of certain direct sums of ‘permutation modules’ over Brauer algebras. Explicit combinatorial bases of these new Schur algebras are given; in particular, these Schur algebras are defined integrally. The new Schur algebras are related to the Brauer algebra by Schur–Weyl dualities on the above sums of permutation modules. Moreover, they are shown to be quasi-hereditary. Over fields of characteristic different from two or three, the new Schur algebras are quasi-hereditary 1-covers of Brauer algebras, and hence the unique ‘canonical’ Schur algebras of Brauer algebras.     

可积代数正规类中半素代数类及半素一致代数类确定的上根

利用代数正规类中的理想乘积公理，引入可积代数正规类及可积代数正规类中素代数、半素代数类及一致代数类概念，讨论了可积代数正规类中半素代数类及半素一致代数类确定的上根性质。     

Graded extended Lie-type algebras

The class of extended Lie-type algebras contains the ones of associative algebras, Lie algebras, Leibniz algebras, dual Leibniz algebras, pre-Lie algebras, and Lie-type algebras, etc. We focus on the class of extended Lie-type algebras graded by an Abelian group G and study its structure, by stating, under certain conditions, a second Wedderburn-type theorem for this class of algebras.     

Twisted Hamiltonian Lie algebras and their multiplicity-free representations

We construct a class of new Lie algebras by generalizing the one-variable Lie algebras generated by the quadratic conformal algebras (or corresponding Hamiltonian operators) associated with Poisson algebras and a quasi-derivation found by Xu. These algebras can be viewed as certain twists of Xu’s generalized Hamiltonian Lie algebras. The simplicity of these algebras is completely determined. Moreover, we construct a family of multiplicity-free representations of these Lie algebras and prove their irreducibility.     

关于局部顶点李代数的一些注记

本文研究局部顶点李代数与顶点代数之间的关系.利用由局部顶点李代数构造顶点代数的方法,定义局部顶点李代数之间的同态,证明了同态可以唯一诱导出由局部顶点李代数构造所得到的顶点代数之间的同态.     

Infinite-dimensional 3-Lie algebras and their connections to Harish-Chandra modules

We construct two kinds of infinite-dimensional 3-Lie algebras from a given commutative associative algebra, and show that they are all canonical Nambu 3-Lie algebras. We relate their inner derivation algebras to Witt algebras, and then study the regular representations of these 3-Lie algebras and the natural representations of the inner derivation algebras. In particular, for the second kind of 3-Lie algebras, we find that their regular representations are Harish-Chandra modules, and the inner derivation algebras give rise to intermediate series modules of the Witt algebras and contain the smallest full toroidal Lie algebras without center.     

一类特征单的n-李代数

利用结合代数与n-李代数的张量积构造了一类无限维特征单的n-李代数,且证明了除n=3的情形以外,这类特征单n-李代数的内导子代数是特征单李代数.     

Centroids of Zinbiel Algebras

Zinbiel algebras were introduced by a way of Koszul dual to Leibniz algebras and connected with commutative associate algebras, pre-Lie algebras and dendriform algebras etc. In this article, the centroids of Zinbiel algebra are discussed. We study the proprieties of centroids and also determinate the centroids of Zinbiel algebras up to dimension ≤4. As consequent, we get the conclusion that the centroids of 2-dimensional Zinbiel algebras are not small and 3,4-dimensional Zinbiel algebras are almost small.