Non-degenerate graded Lie algebras with a degenerate transitive subalgebra

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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.
21 pages

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Rings and Algebras, 17B05, 17B20, 17B50, 17B70

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http://salesiana.dossiersoluciones.com/handle/123456789/219943

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0901.4525
 http://arxiv.org/abs/0901.4525

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arXiv