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 ...

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 ...

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...

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...

We define regular Kac-Moody superalgebras and classify them using integrable modules. We give conditions for irreducible highest weight modules of regular Kac-Moody superalgebras to be integrable. This paper is a major part of the proof for the classification of finite-growth contragredient Lie superalgebras. The results of this paper are a crucial part of the proof for the classification of co...

We define regular Kac-Moody superalgebras and classify them using integrable modules. We give conditions for irreducible highest weight modules of regular Kac-Moody superalgebras to be integrable. This paper is a major part of the proof for the classification of finite-growth contragredient Lie superalgebras. The results of this paper are a crucial part of the proof for the classification of co...

We continue the study of irreducible representations of the exceptional Lie superalgebra E(3, 6). This is one of the two simple infinite-dimensional Lie superalgebras of vector fields which have a Lie algebra sl(3) × sl(2) × gl(1) as the zero degree component of its consistent Z-grading. We provide the classification of the singular vectors in the degenerate Verma modules over E(3, 6), completi...

In this work, we study direct limits of finite dimensional basic classical simple Lie superalgebras and obtain the conjugacy classes of Cartan subalgebras under the group of automorphisms.

Making use of a Howe duality involving the infinite-dimensional Lie superalgebra ĝl∞|∞ and the finite-dimensional group GLl of [CW3] we derive a character formula for a certain class of irreducible quasi-finite representations of ĝl∞|∞ in terms of hook Schur functions. We use the reduction procedure of ĝl∞|∞ to ĝln|n to derive a character formula for a certain class of level 1 highest weight ir...