Hamiltonian type Lie bialgebras

We first prove that,for any generalized Hamiltonian type Lie algebra H,the first co- homology group H~1(H,H(?)H) is trivial.We then show that all Lie bialgebra structures on H are triangular.     

三维幂零李超代数的Yang-Baxter算子

在复数域C上,利用三维幂零李超代数的分类,通过计算刻画了三维幂零李超代数的Yang-Baxter算子.     

线状李超代数Ln,m上的Yang-Baxter 方程

在特征零的代数闭域上,首先做出Ln,m 的一个空间的直和分解,从而将Ln,m 上的Yang-Baxter 方程的解分为若干情形。然后分别在每种情形下对Yang-Baxter 方程进行求解,进而得到了Ln,m 上的所有的Yang-Baxter方程的解的矩阵形式。     

Hom-泊松代数与Hom-泊松杨巴克斯特方程

本文介绍Hom-泊松双代数的概念,给出Hom-泊松代数的Manin三元组的等价性描述.其次引入上边缘Hom-泊松双代数的概念,从而构造出Hom-泊松杨巴克斯特方程的解.     

四维Filiform李超代数的Yang-Baxter方程

利用复数域C上四维Filiform李超代数的分类,通过计算刻画了复数域C上四维Filiform李超代数上的所有Yang-Baxter方程的解.     

Yang-Baxter方程的解与量子Yang-Baxter H-余模

设Ｈ是域ｋ上的Ｈｏｐｆ代数。本文首先讨论了量子Ｙａｎｇ－Ｂａｘｔｅｒ Ｈ－余模与Ｙａｎｇ－Ｂａｘｔｅｒ方程的解的关系;然后作为应用,给出了任意Ｈｏｐｆ代数上Ｙａｎｇ－Ｂａｘｔｅｒ方程的一个解。     

Filiform李超代数L_(1,2)上的Yang-Baxter方程

求解一般Filiform李超代数L_(n,m)的Yang-Baxter方程尚无一般方法.通过计算,刻画了特征零的代数闭域上四维Filiform李超代数L_(1,2)上的所有Yang-Baxter方程的解.     

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.     

Lie Bialgebras of Generalized Loop Virasoro Algebras

The first cohomology group of generalized loop Virasoro algebras with coefficients in the tensor product of its adjoint module is shown to be trivial. The result is used to prove that Lie bialgebra structures on generalized loop Virasoro algebras are coboundary triangular. The authors generalize the results to generalized map Virasoro algebras.     

Lie bialgebra structures on generalized loop Schr?dinger-Virasoro algebras

We give a classification of Lie bialgebra structures on generalized loop Schr?dinger-Virasoro algebras st). Then we find out that not all Lie bialgebra structures on generalized loop Schr?dinger-Virasoro algebras st) are triangular coboundary.     

Super solutions of the dynamical Yang-Baxter equation

Solutions of the classical dynamical Yang-Baxter equation on a Lie superalgebra are called super dynamical matrices. A super dynamical matrix satisfies the zero weight condition if

    for all 

In this paper we classify super dynamical matrices with zero weight.

     

Compatible Poisson Brackets on Lie Algebras

We discuss the relationship between the representation of an integrable system as an L-A-pair with a spectral parameter and the existence of two compatible Hamiltonian representations of this system. We consider examples of compatible Poisson brackets on Lie algebras, as well as the corresponding integrable Hamiltonian systems and Lax representations.     

弱准三角Hopf代数和解量子Yang-Baxter方程

出于解量子Yang-Baxter方程的需要,本文定义了弱准三角Hopf代数,并且发现了一类构造弱准三角Hopf代数的方法,文中称之为杨-积,它可以提供量子Yang-Baxter方程的解.     

Lie Bialgebras of a Family of Lie Algebras of Block Type

Lie bialgebra structures on a family of Lie algebras of Block type are shown to be triangular coboundary.     

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.     

Compatible Lie Brackets and Integrable Equations of the Principal Chiral Model Type

We consider two classes of integrable nonlinear hyperbolic systems on Lie algebras. These systems generalize the principal chiral model. Each system is related to a pair of compatible Lie brackets and has a Lax representation, which is determined by the direct sum decomposition of the Lie algebra of Laurent series into the subalgebra of Taylor series and the complementary subalgebra corresponding to the pair. New examples of compatible Lie brackets are given.     

Lie super-bialgebra structures on super-Virasoro algebra

In this paper we obtain that every super-Virasoro algebra admits only triangular coboundary Lie super-bialgebra structures and this is proved mainly based on the computation of derivations from the super-Virasoro algebra to the tensor product of its adjoint module.      

Lie bialgebras of generalized Witt type

In this paper, all Lie bialgebra structures on the Lie algebras of generalized Witt type are considered. It is proved that, for any Lie algebra W of generalized Witt type, all Lie bialgebras on W are the coboundary triangular Lie bialgebras. As a by-product, it is also proved that the first cohomology group H1(W, W(?)W) is trivial.