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

Abstract

In this paper, a finite-dimensional Lie superalgebra $K\left(n,m\right)$ over a field of prime characteristic is constructed. Then, we study some properties of $K\left(n,m\right)$ . Moreover, we prove that $K\left(n,m\right)$ 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.