Schrodinger-Virasoro型李共形代数的共形双导子和自同构群北大核心CSCD

本文确定了两类Schrodinger-Virasoro型李共形代数TSV(a,b)和TSV(c)的共形双导子和自同构群.作为主要定理的推论,本文得到了李共形代数W(a,b)的共形双导子和自同构群.     

经典N=2李共形超代数的导子和第二上同调群

研究了经典N=2李共形超代数的导子和第二上同调群的结构,并应用第二上同调群的结果确定了该李共形超代数的泛中心扩张.     

Schrdinger Virasoro李共形代数

该文利用形式分布李代数的相关结论,详细刻划并分类了一类与Schrdinger Virasoro李代数相关的秩为3的李共形代数的结构.所考虑到的Schrdinger Virasoro李共形代数是一类以{L_n,I_n,Y_n|n∈Z}为基的李代数,其中基元素之间的关系式是[L_m,L_n]=(m-n)L_(m+n),[L_m,I_n]=-nI_(m+n),[L_m,Y_n]=(m/2-n)Y_(m+n),[Y_m,I_n]=[I_m,I_n]=0,[Y_m,Y_n]=(m-n)I_(m+n).     

Schrdinger Virasoro李共形代数

该文利用形式分布李代数的相关结论,详细刻划并分类了一类与Schrdinger Virasoro李代数相关的秩为3的李共形代数的结构.所考虑到的Schrdinger Virasoro李共形代数是一类以{L_n,I_n,Y_n|n∈Z}为基的李代数,其中基元素之间的关系式是[L_m,L_n]=(m-n)L_(m+n),[L_m,I_n]=-nI_(m+n),[L_m,Y_n]=(m/2-n)Y_(m+n),[Y_m,I_n]=[I_m,I_n]=0,[Y_m,Y_n]=(m-n)I_(m+n).     

两类N=2超共形代数上的超双导子和超交换映射

确定广义Topological N=2超共形代数和Twisted N=2超共形代数上的超斜对称双导子.证明在这两类超代数上的所有超双导子都是超双内导子.应用此结论,得到在广义Topological N=2超共形代数上的线性超交换映射是非标准的,而Twisted N=2超共形代数上的线性超交换映射是标准的.     

psl(∧(2|2))(2)k 非线性σ-模型超对称性质研究

由psl(∧(2|2))(2)k非线性σ-模型加上WZ-项得到的WZW模型是共形场论,它具有李超代数psi(2|2)对称性.该文用向量相干态方法给出了李超代数psl(2|2)的微分算子表示.并在此基础上给出了扭曲Kac-Moody李超代数psl(∧(2|2))(2)k自由场实现,相应共形场论的中心荷为-2.     

psl（2｜2）^（2）k非线性σ-模型超对称性质研究

由psl（2｜2）^（2）k非线性σ-模型加上WZ-项得到的WZW模型足共形场论,它具有李超代数psl（2｜2）对称性.该文用向量相干态方法给出了李超代数psl（2｜2）的微分算子表示.并在此基础上给出了扭曲Kac-Moody李超代数psl（2｜2）^（2）k自由场实现,相应共形场论的中心荷为-2.     

共形空间中有两个共形主曲率的共形等参超曲面

研究了共形空间中正则超曲面的共形几何,并在共形等价意义下对有两个共形主曲率的共形等参超曲面作了分类.     

共形空间中具有平行的共形第二基本形式的I型类时超曲面的分类

共形空间中具有平行的共形第二 基本形式的类空超曲面已经作了完全分类, 本文将继续类时情形的探讨并对此时的I型 类时超曲面分类.       

Topological超共形代数的Leibniz中心扩张

通过计算得到了Topological N=2超共形代数丁的Leibniz二上同调群,从而确定了此代数的Leibniz中心扩张.     

Simplicity of quadratic Lie conformal algebras

In this paper, simplicity of quadratic Lie conformal algebras is investigated. From the view point of the corresponding Gel’fand–Dorfman bialgebras, some su?cient conditions and necessary conditions to ensure simplicity of quadratic Lie conformal algebras are presented. By these observations, we present several new classes of infinite simple Lie conformal algebras. These results will be useful for classification purposes.     

Universal enveloping conformal algebras

The main objective of this paper is to study embeddings of Lie conformal algebras into associative conformal algebras. We prove that not all Lie conformal algebras admit such embeddings. However, in many important cases, including semisimple Lie conformal algebras of finite type, embeddings of this form exist and sometimes we can even describe universal enveloping associative conformal algebras of Lie conformal algebras and prove an analogue of the classical Poincaré-Birkhoff-Witt theorem.     

Varieties of dialgebras and conformal algebras

We introduce and study the concept of a variety of dialgebras which is closely related to the concept of a variety of conformal algebras: Each dialgebra of a given variety embeds into an appropriate conformal algebra of the same variety. In particular, the Leibniz algebras are exactly Lie dialgebras, and each Leibniz algebra embeds into a conformal Lie algebra.     

Gröbner–Shirshov Bases: From their Incipiency to the Present

In this paper, the history and the main results of the theory of Gröbner–Shirshov bases are given for commutative, noncommutative, Lie, and conformal algebras from the beginning (1962) to the present time. The problem of constructing a base of a free Lie algebra is considered, as well as the problem of studying the structure of free products of Lie algebras, the word problem for Lie algebras, and the problem of embedding an arbitrary Lie algebra into an algebraically closed one. The modern form of the composition-diamond lemma (the CD lemma) is presented. The rewriting systems for groups are considered from the point of view of Gröbner–Shirshov bases. The important role of conformal algebras is treated, the statement of the CD lemma for associative conformal algebras is given, and some examples are considered. An analog of the Hilbert basis theorem for commutative conformalalgebras is stated. Bibliography: 173 titles.     

Some General Results on Conformal Embeddings of Affine Vertex Operator Algebras

We give a general criterion for conformal embeddings of vertex operator algebras associated to affine Lie algebras at arbitrary levels. Using that criterion, we construct new conformal embeddings at admissible rational and negative integer levels. In particular, we construct all remaining conformal embeddings associated to automorphisms of Dynkin diagrams of simple Lie algebras. The semisimplicity of the corresponding decompositions is obtained by using the concept of fusion rules for vertex operator algebras.     

Polynomial Lie Algebras and Growth of Their Finitely Generated Lie Subalgebras

The concept of polynomial Lie algebra of finite rank was introduced by V. M. Buchstaber in his studies of new relationships between hyperelliptic functions and the theory of integrable systems. In this paper we prove the following theorem: the Lie subalgebra generated by the frame of a polynomial Lie algebra of finite rank has at most polynomial growth. In addition, important examples of polynomial Lie algebras of countable rank are considered in the paper. Such Lie algebras arise in the study of certain hyperbolic partial differential equations, as well as in the construction of self-similar infinite-dimensional Lie algebras (such as the Fibonacci algebra).     

Steinberg unitary Lie conformal algebras

In this paper, we study Steinberg unitary Lie conformal algebras, which are universal central extensions of unitary Lie conformal algebras. We describe the kernels of these extensions by means of skew-dihedral homology. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 2, pp. 135–155, 2005.     

On Schrödinger-Virasoro type Lie conformal algebras

In this paper, two classes of Schrödinger-Virasoro type Lie conformal algebras TSV(a,b) and TSV(c) which are non-simple are introduced for some a, b, c∈?. Moreover, central extensions, conformal derivations and free conformal modules of rank 1 of TSV(a,b) and TSV(c) are determined.