On the toroidal Leibniz algebras

Toroidal Leibniz algebras are the universal central extensions of the iterated loop algebras g×C[t1^±1,...,tv^±1] in the category of Leibniz algebras. In this paper, some properties and representations of toroidal Leibniz algebras are studied. Some general theories of central extensions of Leibniz algebras are also obtained.     

Derivation algebra and automorphism group of generalized topological N = 2 superconformal algebra

We determine the derivation algebra and the automorphism group of the generalized topological N = 2 superconformal algebra.     

Derivation algebra and automorphism group of generalized Ramond N = 2 superconformal algebra

In this paper, we give the definition of the generalized Ramond N = 2 superconformal algebras and discuss the derivation algebra and the automorphism group.     

Virasoro—相似代数的导子代数

本文给出了Ｖｒａｓｏｒｏ－相似 代数的导子代数及导子代的自同构群。     

中心为4的8维幂零李代数的分类

In this paper, we give a complete classification of eight dimensional nilpotent Lie algebras with four-dimensional center by using the method of Skjelbred and Sund.     

Strictly nontame primitive elements of the free metabelian Lie algebra of rank 3

We prove that the free metabelian Lie algebra M ₃ of rank 3 over an arbitrary field K admits strictly nontame primitive elements.     

Graded automorphism group of TKK algebra

The classification of extended affine Lie algebras of type A_1 depends on the Tits-Kantor- Koecher (TKK) algebras constructed from semilattices of Euclidean spaces.One can define a unitary Jordan algebra J(S) from a semilattice S of R~v (v≥1),and then construct an extended affine Lie algebra of type A_1 from the TKK algebra T(J(S)) which is obtained from the Jordan algebra J(S) by the so-called Tits-Kantor-Koecher construction.In R~2 there are only two non-similar semilattices S and S′,where S is a lattice and S′is a non-lattice semilattice.In this paper we study the Z~2-graded automorphisms of the TKK algebra T(J(S)).     

Automorphism group and representation of a twisted multi-loop algebra

Let G be the complexification of the real Lie algebra so（3） and A = C[t1^±1, t2^±1] be the Lau-ent polynomial algebra with commuting variables. Let L：（t1, t2, 1） = G c .A be the twisted multi-loop Lie algebra. Recently we have studied the universal central extension, derivations and its vertex operator representations. In the present paper we study the automorphism group and bosonic representations ofL（t1, t2, 1）.     

可换环上Abel李代数的全形的导子和自同构

决定了可换环上Abel李代数的全形的导子代数和自同构群.     

Universal Central Extensions of Lie Groups

We call a central Z-extension of a group G weakly universal for an Abelian group A if the correspondence assigning to a homomorphism ZA the corresponding A-extension yields a bijection of extension classes. The main problem discussed in this paper is the existence of central Lie group extensions of a connected Lie group G which is weakly universal for all Abelian Lie groups whose identity components are quotients of vector spaces by discrete subgroups. We call these Abelian groups regular. In the first part of the paper we deal with the corresponding question in the context of topological, Fréchet, and Banach–Lie algebras, and in the second part we turn to the groups. Here we start with a discussion of the weak universality for discrete Abelian groups and then turn to regular Lie groups A. The main results are a Recognition and a Characterization Theorem for weakly universal central extensions.     

Generalized Heisenberg-Virasoro algebras

In this paper, we mainly study the generalized Heisenberg-Virasoro algebra. Some structural properties of the Lie algebra are obtained.      

Graded automorphism group of TKK Lie algebra over semilattice

Every extended affine Lie algebra of type A ₁ and nullity ν with extended affine root system R(A ₁, S), where S is a semilattice in ℝ ^ν , can be constructed from a TKK Lie algebra T (J (S)) which is obtained from the Jordan algebra J (S) by the so-called Tits-Kantor-Koecher construction. In this article we consider the ℤ ⁿ -graded automorphism group of the TKK Lie algebra T (J (S)), where S is the “smallest” semilattice in Euclidean space ℝ ⁿ .     

Derivations and extensions of lie color algebra

In this article,the authors obtain some results concerning derivations of finitely generated Lie color algebras and discuss the relation between skew derivation space SkDer（L）and central extension H^2（L,F）on some Lie color algebras.Meanwhile,they generalize the notion of double extension to quadratic Lie color algebras,a sufficient condition for a quadratic Lie color algebra to be a double extension and further properties are given.     

以幂零李代数R_n为幂零根基的可解李代数(英文)

In this paper we explicitly determine automorphism group of filiform Lie algebra Rn to find the indecomposable solvable Lie algebras with filiform Lie algebra Rn nilradicals.We also prove that the indecomposable solvable Lie algebras with filiform Rn nilradicals is complete.     

三角导子李代数的中心扩张

In this paper,we study a class of subalgebras of the Lie algebra of vector fields on n-dimensional torus,which are called the Triangular derivation Lie algebra.We give the structure and the central extension of Triangular derivation Lie algebra.     

Color cyclic homology and Steinberg Lie color algebras

The present paper contains two interrelated developments. First, the basic properties of the construction theory over the Steinberg Lie color algebras are developed in analogy with Steinberg Lie algebra case. This is done on the example of the central closed of the Steinberg Lie color algebras. The second development is that we define the first ?-cyclic homology group HC₁(R, ?) of the Γ-graded associative algebra R (which could be seemed as the generalization of cyclic homology group and the ?/2?-graded version of cyclic homology that was introduced by Kassel) to calculate the universal central extension of Steinberg Lie color algebras.     

Left-symmetric algebra structures on the twisted Heisenberg-Virasoro algebra

The compatible left-symmetric algebra structures on the twisted Heisenberg-Virasoro algebra with some natural grading conditions are completely determined. The results of the earlier work on left-symmetric algebra structures on the Virasoro algebra play an essential role in determining these compatible structures. As a corollary, any such left-symmetric algebra contains an infinite-dimensional nontrivial subalgebra that is also a submodule of the regular module.