%0 Journal Article
%T Non-degenerate graded Lie algebras with a degenerate transitive subalgebra
%A Thomas B. Gregory
%A Michael I. Kuznetsov
%J Mathematics
%D 2009
%I arXiv
%X The property of degeneration of modular graded Lie algebras, first investigated by B. Weisfeiler, is analyzed. Transitive irreducible graded Lie algebras $L=\sum_{i\in \mathbb Z}L_i,$ over an algebraically closed field of characteristic $p>2,$ with classical reductive component $L_0$ are considered. We show that if a non-degenerate Lie algebra $L$ contains a transitive degenerate subalgebra $L'$ such that $\dim L'_1>1,$ then $L$ is an infinite-dimensional Lie algebra.
%U http://arxiv.org/abs/0901.4525v2