let $mathbb{f}$ be an algebraically closed field of prime characteristic $p>2$ and $(g, [p])$ a finite-dimensional restricted lie superalgebra over $mathbb{f}$. it is showed that anyfinite-dimensional indecomposable $g$-module is a module for a finite-dimensional quotient of the universal enveloping superalgebra of $g$. these quotient superalgebras are called the generalized reduced enveloping ...

In this paper we review the concepts of the superalgebra, superderivation and some properties of them. We will define algebraic and differential superderivations on a superalgebra and will prove some theorems about them, Then we consider a superalgebra bundle, that is an algebra bundle which its fibers are superalgebras and then characterize the superderivations of the algebra of sections of th...

Let $mathbb{F}$ be an algebraically closed field of prime characteristic $p>2$ and $(g, [p])$ a finite-dimensional restricted Lie superalgebra over $mathbb{F}$. It is showed that anyfinite-dimensional indecomposable $g$-module is a module for a finite-dimensional quotient of the universal enveloping superalgebra of $g$. These quotient superalgebras are called the generalized reduced enveloping ...

In this paper we use the Etingof-Kazhdan quantization of Lie bisuperalgebras to investigate some interesting questions related to DrinfeldJimbo type superalgebra associated to a Lie superalgebra of classical type. It has been shown that the D-J type superalgebra associated to a Lie superalgebra of type A-G, with the distinguished Cartan matrix, is isomorphic to the E-K quantization of the Lie s...

Associated to the two types of finite dimensional simple superalgebras, there are the general linear Lie superalgebra and the queer Lie superalgebra. The universal enveloping algebras of these Lie superalgebras act on the tensor spaces of the natural representations and, thus, define certain finite dimensional quotients, the Schur superalgebras and the queer Schur superalgebra. In this paper, w...

Recent work applying higher gauge theory to the superstring has indicated the presence of ‘higher symmetry’. Infinitesimally, this is realized by a ‘Lie 2-superalgebra’ extending the Poincaré superalgebra in precisely the dimensions where the classical superstring makes sense: 3, 4, 6 and 10. In the previous paper in this series, we constructed this Lie 2-superalgebra using the normed division ...

A contragredient Lie superalgebra is a superalgebra defined by a Cartan matrix. In general, a contragredient Lie superalgebra is not finite dimensional, however it has a natural Z-grading by finite dimensional components. A contragredient Lie superalgebra has finite growth if the dimensions of these graded components depend polynomially on the degree. We discuss the classification of finite-gro...

We present a geometric formulation of type-IIA and -IIB superstring theories in which the WessZumino term is second order in the supersymmetric currents. The currents are constructed using supergroup manifolds corresponding to superalgebras: the IIA superalgebra derived from M-algebra and the IIB superalgebra obtained by a T-duality transformation of the IIA superalgebra. We find that a slight ...

The Dirac theory in the Euclidean Taub-NUT space gives rise to a large collection of conserved operators associated to genuine or hidden symmetries. They are involved in interesting algebraic structures as dynamical algebras or even infinite-dimensional algebras or superalgebras. One presents here the infinite-dimensional superalgebra specific to the Dirac theory in manifolds carrying the Gross...

The Dirac theory in the Euclidean Taub-NUT space gives rise to a large collection of conserved operators associated to genuine or hidden symmetries. They are involved in interesting algebraic structures as dynamical algebras or even infinite-dimensional algebras or superalgebras. One presents here the infinite-dimensional superalgebra specific to the Dirac theory in manifolds carrying the Gross...