有限维实单Balinsky-Novikov超代数的分类

有限维Balinsky-Novikov超代数可以看作是Novikov代数的一类超模拟,其仿射化给出了一类重要的无限维李超代数.本文主要叙述了它们的一些性质,并给出了实数域上有限维单Balinsky-Novikov超代数的完全分类.

Inhomogeneous Differential Realization, Boson-Fermion Realization of OSP(2,1) Superalgebra and Its Representations

Homogeneous and inhornogeneous differential realizations of the OSP(2,1)superalgebra on the spaces of homogeneous and inhomogeneous polynomials and the corresponding boson-fermioii realizations are studied.The new indecomposable and irreducible representations of the OSP(2,1)are given on subspaces and quotient spaces of the universal enveloping algebras of Heisenberg-Weyl superalgebra.All the finite dimensional irreducible representation of the OSP(2,1)superalgebra is naturally obtained as special cases.

DERIVATION ALGEBRAS OF THE MODULAR LIE SUPERALGEBRAS W AND S OF CARTAN-TYPE

Let F be a field and char F = p > 3. In this paper the derivation algebras of Lie superalgebras W and S of Cartan-type over F are determined by the calculating method.

SOME RESULTS OF MODULAR LIE SUPERALGEBRAS

In the present article, the authors give some properties on subinvariant subalgebras of modular Lie superalgebras and obtain the derivation tower theorem of modular Lie superalgebras, which is analogous to the automorphism tower theorem of finite groups. Moreover, they announce and prove some results of modular complete Lie superalgebras.

Filtration Structure of Finite-Dimensional Special Odd Hamiltonian Superalgebras in Prime Characteristic

The filtration structure of finite-dimensional special odd Hamilton superalgebras over a field of prime characteristic was studied. By determining ad-nilpotent dements in the even part, the natural filtration of special odd Hamiltonian superalgebras is proved to be invariant. Using this result, the special odd Hamilton superalgebras is classified. Finally, the automorphism group of the restricted special odd Hamilton superalgebras is determined.

A Matrix Representation of Outer Derivations from gl0|2 to the Generalized Witt Lie Superalgebra

Let gl0|2 be a subalgebra of the general linear Lie superalgebra.In this paper,outer derivations from gl0|2 to the generalized Witt Lie superalgebra are completely determined by matrices.

Induced Modules of Restricted Lie Superalgebras

In this paper we first prove the PBW theorem for reduced universal enveloping algebras of restricted Lie superalgebras. Then the notion of an induced module is introduced and the dimension formula of induced modules is established. Finally, using the results above, we obtain a property of induced modules pertaining to automorphisms of Lie superalgebras and isomorphisms of modules.

On the Cohomology of Associative Superalgebras

This paper presents a sufficient condition for the cohomology groups of an associative superalgebra to vanish. As its application, we prove that the cohomology groups H n(L,M) vanish when L is a strongly semisimple Lie superalgebra and M is an irreducible faithful L module.

A Linear Combination of Superderivations on Prime Superalgebras

In the paper, we give some results about a linear combination of superderivations on prime superalgebras and generalize a result of Niu Feng-wen.

On Hom-Lie Pseudo-Superalgebras

The aim of this article is to introduce the notion of Hom-Lie H-pseudo-superalgebras for any Hopf algebra H. This class of algebras is a natural generalization of the Hom-Lie pseudo-algebras as well as a special case of the Hom-Lie superalgebras. We present some construction theorems of Hom-Lie H-pseudo-superalgebras, reformulate the equivalent definition of Hom-Lie H-pseudo-super-algebras, and consider the cohomology theory of Hom-Lie H-pseudo-superalgebras with coefficients in arbitrary Hom-modules as a generalization of Kac’s result.

Off-shell BRST-VSUSY Superalgebra for D = 4 BF Theories in Superconnection Formalism

We propose the supereonneetion formalism to construct the off-shell BRST-VSUSY superalgebra for D = 4 BF theories. The method is based on the natural introduction of physical fields as well as auxiliary fields via supereon- neetions and their associated supereurvatures defined on a superspaee. We also give a prescription to build the off-shell BRST-VSUSY exact quantum action.

EMBEDDING THEOREM OF FILTERED LIE SUPERALGEBRAS

The homomorphic realization of Lie superalgebras and the embedding theorem of filtered Lie superalgebras are given and proved.

A Note on Complete Color Lie Superalgebras

We prove that each finitely generated (as a module) complete color Lie superalgebras over noetherian ring can be decomposed uniquely into a direct sum of complete simple ideals.

A new eight-dimensional Lie superalgebra and two corresponding hierarchies of evolution equations

A new eight-dimensional Lie superalgebra is constructed and two isospectral problems with six potentials are designed. Corresponding hierarchies of nonlinear evolution equations, as well as super-AKNS and super-Levi, are derived. Their super-Hamiltonian structures are established by making use of the supertrace identity, and they are integrable in the sense of Liouville.

The Decomposition and Uniqueness of n-Lie Superalgebras

In this paper, the definitions and some properties of n-Lie superalgebras are presented. Our main aim is to study the decomposition and uniqueness of finite dimensional n-Lie superalgebras with trivial center. Aecoding to the decomposition of n-Lie superalgebras, we obtain the decomposition of inner derivation superalgebras and derivation superalgebras respectively. Furthermore, we discuss some properties about the centroid of n-Lie superalgebras, so we can see its application in the decomposition of n-Lie superalgebras.

Transitive filtration of Lie superalgebras

Let L be a finite dimensional simple Lie superalgebra, and a sufficient condition is obtained for the length of transitive filtration of L to be greater than zero.

Infinite-Dimensional Lie Superalgebras SHO' over a Field of Prime Characteristic

The natural filtrations of the infinite-dimensional modular Lie superalgebra SHO＇ are proved to be invariant under automorphisms of SHO＇. The proof involves the investigation of the ad-nilpotent elements of the even part, and the determination of the subalgebras generated by certain ad-nilpotent elements. A property of automorphisms of these Lie superalgebras can be established, and an intrinsic characterization of SHO＇ can be obtained.

Hom-Leibniz Superalgebras

We gived the definition of Hom-Leibniz superalgebra and studied its basic properties. In particular, the derivations of Hom-Leibniz Superalgebras are portrayed in detail.

COHERENT STATE REPRESENTATION OF THE LIE SUPERALGEBRA OSP(1,2)

We construct coherent states associated with the Lie superalgebra OSP(1. 2) with the aid of two SU(2) coherent states and discuss their properties in detail. We also evaluate the matrix elements of the OSP(1, 2) generators in the coherent-state representation and give a realization for the OSP(1, 2) generators in the coherent state space.

On Perfect Lie Superalgebras

In this paper, some properties of perfect Lie superalgebras are investigated. We prove that the derivation superalgebra of a centerless perfect Lie superalgebra of arbitrary dimension over a field of arbitrary characteristic is complete and we obtain a necessary and sufficient condition for the holomorph of a centerless perfect Lie superalgebra to be complete. Finally, some properties of perfect restricted Lie superalgebras are given.