The classification of modular Lie superalgebras of type M

Abstract

Abstract: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.

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

“…Given i ∈ Y, let z/zx i be the partial derivative on Λ(n) with respect to x i . For i ∈ Y, let D i be the linear transformation on U such that D i (x u y λ ) � (zx u / zx i )y λ for all u ∈ B(n) and λ ∈ G. Let Der U denote the derivation superalgebra of U (see [11]). en,…”

“…e research on Lie superalgebras over a field of characteristic zero has been quite systematic (see [4][5][6]), but the research on modular Lie superalgebras remains to be perfected (see [7]). Although some mathematicians try to study the classification of modular Lie superalgebras (see [7][8][9][10][11][12][13]), the classification problem has still been open. erefore, it is very important to construct new finite-dimensional modular Lie superalgebras.…”