Constructions and Properties for a Finite-Dimensional Modular Lie Superalgebra K n , m

In this paper, a finite-dimensional Lie superalgebra K n , m over a field of prime characteristic is constructed. Then, we study some properties of K n , m . Moreover, we prove that K n , m is an extension of a simple Lie superalgebra, and if m = n − 1 , then it is isomorphic to a subalgebra of a restricted Lie superalgebra.

The Even Part of Finite-Dimensional Modular Lie Superalgebra Γ

Let [Formula: see text] be the underlying base field of characteristic [Formula: see text] and denote by [Formula: see text] the even part of the finite-dimensional Lie superalgebra [Formula: see text]. We give the generator sets of the Lie algebra [Formula: see text]. Using certain properties of the canonical tori of [Formula: see text], we describe explicitly the derivation algebra of [Formula: see text].

The classification of modular Lie superalgebras of type M

The natural filtration of the infinite-dimensional simple modular Lie superalgebra M over a field of characteristic p > 2 is proved to be invariant under automorphisms by discussing ad-nilpotent elements. Moreover, an intrinsic property is obtained and all the infinite-dimensional simple modular Lie superalgebras M are classified up to isomorphisms. As an application, a property of automorphisms of M is given.

A Note on the Cartan Type Lie Superalgebra $\widetilde{S}(n)$ over a Field of Positive Characteristic

The main result of this paper is that every derivation of the finite-dimensional simple modular Lie superalgebra [Formula: see text] is inner, and [Formula: see text] has no nonsingular associative form.

The Natural Filtration of Finite Dimensional Modular Lie Superalgebras of Special Type

This paper is concerned with the natural filtration of Lie superalgebraS(n,m)of special type over a field of prime characteristic. We first construct the modular Lie superalgebraS(n,m). Then we prove that the natural filtration ofS(n,m)is invariant under its automorphisms.