一般线性李超代数及其超群的无穷小子群的表示

在索特征代数闭域上考虑一般线性李超代数gl(m |n)的限制表示与超群GL(m | n)的有理表示以及它们的关系.主要结果为: (1)对gl(m | n)的不可约限制表示进行分类,其中某些单模恰是Kac-模.类似于复数域情形,给出了Kac-模不可约的充要条件; (2)当m≠n(mod p)以及p≥2h-2(h=max{m,n})时,gl(m | n)的限制投射模可以被提升为有理GL(m | n)-模,并且证明了不可约表示的投射覆盖具有Z-滤过,即滤过中的每个子商同构于"baby Vlerma模";(3)得到了一般线性超群G=GL(m | n)的r阶nobenius核的反转公式,它反映了单Gγ-模的投射覆盖的Z-滤过重数与广义baby Verma模的合成因子效之间的关系.     

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.     

The superalgebra of W(2,2) and its modules of the intermediate series

In this paper, we study a new Lie superalgebra constructed by a 2|2-dimensional Balinsky–Novikov superalgebra, which is called the superalgebra of W(2,2). It can be realized from semi product of the W-algebra W(2,2) and its module of the intermediate series. Finally, we determine all modules of the intermediate series over this superalgebra. Since it is di?cult to do so directly, we make it by using modules of the intermediate series over the trivial super extension of the Witt algebra.     

Hopf Superquivers

In this paper, a super version of the Hopf quiver theory is developed. The notion of Hopf superquivers is introduced. It is shown that only the path supercoalgebras of Hopf superquivers admit graded Hopf superalgebra structures. A complete classification of such graded Hopf superalgebras is given. A superquiver setting for general pointed Hopf superalgebras is also built up. In particular, a super version of the Gabriel type theorem and the Cartier-Gabriel decomposition theorem is given.     

广义Poisson超代数的同调与上同调群

给出了广义Poisson超代数的同调和上同调群的基本性质.特别是,通过Hochschild上同调以及长正合列,建立了广义Poisson超代数上同调群的理论,刻画了这种代数的低阶上同调群.最后,决定了5-正合列以及它的泛中心扩张的核.     

Fractional supersymmetric su(2) algebras

In this paper, the third root of the Lie algebra su(2) based on the permutation group S₃ is formulated in the Hopf algebra formalism.     

The Even Part of Finite-Dimensional Modular Lie Superalgebra Г

Let F be the underlying base field of characteristic p ＞ 3 and denote by Γō the even part of the finite-dimensional Lie superalgebra Γ.We give the generator sets of the Lie algebra Γō.Using certain properties of the canonical tori of Γō,we describe explicitly the derivation algebra of Γō.     

DERIVATION ALGEBRAS OF THE MODULAR LIESUPERALGEBRAS W AND S OF CARTAN-TYPE

1NatationandPreliminariesWeknowthatthederivationalgebrasisaveryusefulsubjectintheresearchoftheLiealgebrasandLiesupealgebras.Inpapersl1]and[2]thederivationalgebrasofmodularLiealgebrasofCartan-typeareinyestigaved.Inpaper[3]thederivationalgebrasofsimpleLiesuperalgebrasoverfieldsofcharacteristiczeroaredeterndned.Inthispaperthederivational-gebrasofmodularLiesuperalgebrasWandSofCartan-typearedeterminedbythecalculatingmethod-LetFbeafieldandcharF=p>3-WesimPlydescribetheLiesuperalgbrasWandSwhic…     

Infinite-dimensional primitive linearly compact Lie superalgebras

We classify open maximal subalgebras of all infinite-dimensional linearly compact simple Lie superalgebras. This is applied to the classification of infinite-dimensional Lie superalgebras of vector fields, acting transitively and primitively in a formal neighborhood of a point of a finite-dimensional supermanifold.