Infinite-Dimensional Modular Lie Superalgebra Ω

Abstract

All ad-nilpotent elements of the infinite-dimensional Lie superalgebra $\Omega$ over a field of positive characteristic are determined. The natural filtration of the Lie superalgebra $\Omega$ is proved to be invariant under automorphisms by characterizing ad-nilpotent elements. Then an intrinsic property is obtained by the invariance of the filtration; that is, the integers in the definition of $\Omega$ are intrinsic. Therefore, we classify the infinite-dimensional modular Lie superalgebra $\Omega$ in the sense of isomorphism.