李代数W(2,2)上的Hom-李代数结构

李代数W（2,2）是一类重要的无限维李代数,它是在研究权为2的向量生成的顶点算子代数的过程当中提出来的.Hom-李代数是指同时具备代数结构和李代数结构的一类代数,并且乘法与李代数乘法运算满足Leibniz法则.本文确定了李代数W（2,2）上的Hom-李代数结构.主要结论是李代数W（2,2）上没有非平凡的Hom-李代数结构.本文的研究结果对于W（2,2）代数的进一步研究有一定的帮助作用.     

Lie Bialgebra Structures on Lie Algebras of Generalized Weyl Type

Lie bialgebra structures on Lie algebras of generalized Weyl type are studied. They are shown to be triangular coboundary.     

Witt型与Virasoro型Lie双代数的对偶

本文给出单边的Witt 型、Witt 型和Virasoro 型Lie 双代数的对偶Lie 双代数结构. 由此, 本文得到一系列无限维Lie 代数.     

Dual Coalgebras of Jordan Bialgebras and Superalgebras

W. Michaelis showed for Lie bialgebras that the dual coalgebra of a Lie algebra is a Lie bialgebra. In the present article we study an analogous question in the case of Jordan bialgebras. We prove that a simple infinite-dimensional Jordan superalgebra of vector type possesses a nonzero dual coalgebra. Thereby, we demonstrate that the hypothesis formulated by W. Michaelis for Lie coalgebras fails in the case of Jordan supercoalgebras.     

q-Deformation of W（2, 2） Lie Algebra Associated with Quantum Groups

The q-deformation of W (2, 2) Lie algebra is well defined based on a realization of this Lie algebra by using the famous bosonic and fermionic oscillators in physics. Furthermore, the quantum group structures on the q-deformation of W (2, 2) Lie algebra are completely determined. Finally, the 1-dimensional central extension of the q-deformed W (2, 2) Lie algebra is studied, which turns out to be coincided with the conventional W (2, 2) Lie algebra in the q → 1 limit.     

Structures of Malcev Bialgebras on a Simple Non-Lie Malcev Algebra

In this work we consider Malcev bialgebras. We describe all structures of a Malcev bialgebra on a simple non-Lie Malcev algebra.     

Conformal biderivations of loop W (a,b) Lie conformal algebra

We study conformal biderivations of a Lie conformal algebra. First, we give the definition of a conformal biderivation. Next, we determine the conformal biderivations of loop W(a, b) Lie conformal algebra, loop Virasoro Lie conformal algebra, and Virasoro Lie conformal algebra. Especially, all conformal biderivations on Virasoro Lie conformal algebra are inner conformal biderivations.     

（n-3）-Filiform李代数的极大环面

求出了（n-3）-filiform李代数的极大环面，并证明了（n-3）-filiform李代数是可完备化的．     

李代数L(Z,f,δ)的特殊性质

研究一类特殊的无限维李代数．利用系数矩阵和极大项,证明了这类李代数是半单李代数且没有二维交换子代数．     

Restricted Lie 2-algebras

In this article, we introduce the notions of restricted Lie 2-algebras and crossed modules of restricted Lie algebras, and give a series of examples of restricted Lie 2-algebras. We also construct restricted Lie 2-algebras from A(m)-algebras, restricted Leibniz algebras, restricted right-symmetric algebras. Finally, we prove that there is a one-to-one correspondence between strict restricted Lie 2-algebras and crossed modules of restricted Lie algebras.     

Quantization of Lie bialgebras, II

This paper is a continuation of [EK]. We show that the quantization procedure of [EK] is given by universal acyclic formulas and defines a functor from the category of Lie bialgebras to the category of quantized universal enveloping algebras. We also show that this functor defines an equivalence between the category of Lie bialgebras over k [[h]] and the category of quantized universal enveloping (QUE) algebras.     

n-Derivations of the Extended Schr(o)dinger-Virasoro Lie Algebra

Let (sb～) be the extended Schr(o)dinger-Virasoro Lie algebra and n ≥ 1 an integer.A map f: (sb～)n =(sb～) × (sb～) × … × (sb～) → (sb～) is called an n-derivation if it is a derivation inone variable while other variables fixed.We investigate n-derivations of the extendedSchr(o)dinger-Virasoro Lie algebra (sb～).The main result when n =2 is then applied tocharacterize the linear commuting maps and the commutative post-Lie algebra structureson (sb～).     

G2型2-Toroidal李代数的顶点表示

在[4]和[5]中已经研究了sim p ly-laced型T oro idal李代数的顶点表示,[6]文据此给出了Bl型T oro idal李代数顶点表示的构造.受[6]文启发,本文给出了G2型T oro idal李代数的顶点表示的构造,这种构造方式与D(41)的D ynk in图的顶点粘合和一个2上循环有着紧密联系.     

Finite Dimensional Lie Superalgebras W(m,n,t) and S(m,n,t) of Cartan Type

设Ｌ＝Ｗ或Ｓ，Ｆ是特征数大于２的域．本文证明了Ｆ上的有限维单李超代数Ｌ（ｍ，ｎ，ｔ）的自然滤过是不变的．进而得出了Ｌ（ｍ，ｎ，ｔ）与Ｌ（ｍ′，ｎ′，ｔ′）同构的充要条件是ｍ＝ｍ′，ｎ＝ｎ′和ｔｉ＝τ（ｔ′ｉ），ｉ＝１，２，…，ｍ，这里τ是｛１，２，…，ｍ｝的一个置换．     

M_2(R)上的非线性Lie导子

设R是一个含有单位元的2无扰的交换环,M_2(R)是定义在R上的全矩阵代数,证明了M_2(R)上的每一个非线性Lie导子都可以表示成一个内导子,一个可加诱导导子和一个映所有二次换位子为零的中心映射的和.     

Quantizations of the W-Algebra W（2, 2）

We quantize the W-algebra W(2, 2), whose Verma modules, Harish-Chandra modules, irreducible weight modules and Lie bialgebra structures have been investigated and determined in a series of papers recently.