Invariants for Automorphisms of the Underlying Algebras Relative to Lie Algebras of Cartan Type

Abstract

Let $X$ denote a finite or infinite dimensional Lie algebra of Cartan type $W$, $S$, $H$ or $K$ over a field of characteristic $p ≥ 3$. In this paper it is proved that certain filtrations of the underlying algebras are invariant under the admissible groups relative to Lie algebras of Cartan type $X$.