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Nondegenerate graded lie algebras with degenerate transitive subalgebras

Authors:	T B Gregory M I Kuznetsov

Institution:	(1) Department of Mathematics, The Ohio State University at Mansfield, Mansfield, Ohio 44906, USA;(2) Nizhny Novgorod State University, Nizhny Novgorod, Russia

Abstract:	The property of degeneration of modular graded Lie algebras, first investigated by B. Weisfeiler is analyzed. Transitive irreducible graded Lie algebras $L = \sum\limits_{i \in \mathbb{Z}} {L_i}$ over an algebraically closed field of characteristic p > 2 with classical reductive component L ₀ are considered. We show that if a nondegenerate Lie algebra L containes a transitive degenerate subalgebra L′such that dim L′₁ > 1, then L is an infinite-dimensional Lie algebra. Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 60, Algebra, 2008.

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