Non-degenerate graded Lie algebras with a degenerate transitive subalgebra

Details Non-degenerate graded Lie algebras with a degenerate transitive subalgebra Non-degenerate graded Lie algebras with a degenerate transitive subalgebra

2009-01-28

arxiv.org/abs/0901.4525v2

Mathematics

Rings and Algebras

21 pages

Scientific paper

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.

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