q-类似Virasoro-like代数模的导子

记Lq为两个变量的量子环面上的斜导子李代数,当0≠q∈C为非单位时,Lq就是q-类似Virasoro-like代数.本文给出了文中构造的Lq的模上的导子及一上同调群H^1（Lq,M）.     

一类推广的Virasoro-like李代数

构造了一类无限维李代数,它是Virasoro-like李代数的推广.研究了这类李代数的两类自同构,这两类自同构均关于映射的合成构成自同构群,一类同构于对称群S3,另一类同构于Klein交换群.得到了这类李代数一些特殊的自同态、中心.证明了这类李代数不是半单李代数.     

The derivation algebra and the universal central extension of the q-analog of the virasoro-like algebra *

In this paper, the derivation algebra and the universal central extension of the q-analog of the Virasoro-like algebra are given.     

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.     

Lie bialgebra structures on derivation Lie algebra over quantum tori

We investigate Lie bialgebra structures on the derivation Lie algebra over the quantum torus. It is proved that, for the derivation Lie algebra W over a rank 2 quantum torus, all Lie bialgebra structures on W are the coboundary triangular Lie bialgebras. As a by-product, it is also proved that the first cohomology group H ¹(W, W ? W) is trivial.     

Nonzero level Harish-Chandra modules over the Virasoro-like algebra

In the present paper, we study the nonzero level Harish-Chandra modules for the Virasoro-like algebra. We prove that a nonzero level Harish-Chandra module of the Virasoro-like algebra is a generalized highest weight (GHW for short) module. Then we prove that a GHW module of the Virasoro-like algebra is induced from an irreducible module of a Heisenberg subalgebra.     

Class of representations of skew derivation Lie algebra over quantum torus

Let L be the skew derivation Lie algebra of the quantum torus ℂ_q. In this paper, we give a class of irreducible representations for L with infinite dimensional weight spaces.      

Special polynomials in free framed Lie algebra

A framed Lie algebra is an algebra with two operations which is a Lie algebra with respect to one of these operations. A basic example is a Lie algebra of vector fields on a manifold with connection where the covariant derivative serves as an additional operation. In a free framed Lie algebra, we distinguish a set of special polynomials that geometrically correspond to invariantly defined tensors. A necessary condition of being special is derived, and we presume that this condition is also sufficient. Translated from Algebra i Logika, Vol. 47, No. 5, pp. 571–583, September–October, 2008.     

Computing the test rank of a free solvable Lie algebra

We computed the test rank of a free solvable Lie algebra of finite rank.     

Derivations for even part of finite-dimensional modular Lie superalgebra \tilde \Omega

Y. Z. Zhang and Q. C. Zhang [J. Algebra, 2009, 321: 3601?C3619] constructed a new family of finite-dimensional modular Lie superalgebra $\tilde \Omega $ . Let ?? denote the even part of the Lie superalgebra $\tilde \Omega $ .We first give the generator sets of the Lie algebra ??. Then, we reduce the derivation of ?? to a certain form. With the reduced derivation and a torus of ??, we determine the derivation algebra of ??.     

Test rank of an abelian product of a free Lie algebra and a free abelian Lie algebra

Let F be a free Lie algebra of rank n ≥ 2 and A be a free abelian Lie algebra of rank m ≥ 2. We prove that the test rank of the abelian product F ×A is m. Morever we compute the test rank of the algebra F/g_k( F) ^￠F/\gamma _{k}\left( F\right) ^{^{\prime }}.     

Hyperbolic Kac-Moody algebras of rank 2

We describe the structure of a hyperbolic Kac-Moody algebra of rank 2 treated as a module over a root subalgebra which is isomorphic to a simple 3-dimensional Lie algebra and is associated with an imaginary root.Translated fromAlgebra i Logika, Vol. 33, No. 3, pp. 286–300, May–June, 1994.     

The Heisenberg envelope for the Hochschild algebra of a finite-dimensional lie algebra

We consider some kind of Hopf algebra assigned to any finite-dimensional Lie algebra. This algebra was pointed out by Hochschild. We prove several statements on its embeddings into an algebra of formal power series. In particular, we obtain similar results for Lie algebras. More precisely, a Lie algebra can be embedded into a Lie algebra of special derivations with coefficients in rational functions in (quasi)polynomials.     

A Monster Lie algebra?

This paper defines a remarkable Lie algebra of infinite dimension and rank, and conjectures that it may be related to the Fischer-Griess Monster group.     

Periodic automorphisms of the free Lie algebra of rank 3

We prove that each automorphism of finite order of the free Lie algebra of rank 3 over an algebraically closed field is conjugate to a linear automorphism if the field characteristic fails to divide the automorphism order.     

The Lie algebra of skew-symmetric elements and its application in the theory of Jordan algebras

We prove that the Lie algebra of skew-symmetric elements of the free associative algebra of rank 2 with respect to the standard involution is generated as a module by the elements [a, b] and [a, b]³, where a and b are Jordan polynomials. Using this result we prove that the Lie algebra of Jordan derivations of the free Jordan algebra of rank 2 is generated as a characteristic F-module by two derivations. We show that the Jordan commutator s-identities follow from the Glennie-Shestakov s-identity.     

The solution to the embedding problem of a (differential) Lie algebra into its Wronskian envelope

Any commutative algebra equipped with a derivation may be turned into a Lie algebra under the Wronskian bracket. This provides an entirely new sort of a universal envelope for a Lie algebra, the Wronskian envelope. The main result of this paper is the characterization of those Lie algebras which embed into their Wronskian envelope as Lie algebras of vector fields on a line. As a consequence we show that, in contrast to the classical situation, free Lie algebras almost never embed into their Wronskian envelope.     

The hypercentral structure of the group of unitriangular automorphisms of a free metabelian Lie algebra

We describe the hypercentral structure of the group of unitriangular automorphisms of a free metabelian Lie algebra over an arbitrary field. Using it, we prove that this group admits no faithful representation by matrices over a field provided that the algebra rank is at least four.     

Whittaker modules for the derivation Lie algebra of torus with two variables

Let L be the derivation Lie algebra of C[t±11,t±12].Given a triangle decomposition L=L~+⊕h⊕L~-,we define a nonsingular Lie algebra homomorphism ψ:L~+→C and the universal Whittaker L-module W_ψ of type ψ.We obtain all Whittaker vectors and submodules of W_ψ.Moreover,all simple Whittaker L-modules of type ψ are determined.     

无扭算子李代数g(G,M)的子代数

由算子构成的李代数在李代数理论中具有重要的应用,因而研究算子李代数及其子代数的代数结构就显得尤为重要.首先构造了无扭算子李代数g(G,M)的子代数L_1,L_2,g1,g2,然后给出了这些子代数的代数结构及一些重要应用.