Non-degenerate graded Lie algebras with a degenerate transitive subalgebra
Abstract
The property of degeneration of modular graded Lie algebras, first investigated by B. Weisfeiler, is analyzed. Transitive irreducible graded Lie algebras L=Σi∈ ZLi, over an algebraically closed field of characteristic p>2, with classical reductive component L0 are considered. We show that if a non-degenerate Lie algebra L contains a transitive degenerate subalgebra L' such that L'1>1, then L is an infinite-dimensional Lie algebra.
0