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Zbl 0555.17003
Weisfeiler, Boris
On subalgebras of simple Lie algebras of characteristic $p>0$. (English)
[J] Trans. Am. Math. Soc. 286, 471-503 (1984). ISSN 0002-9947; ISSN 1088-6850/e

This paper studies subalgebras of a simple finite-dimensional Lie algebra L over an algebraically closed field of characteristic $p\ge 7$, especially subalgebras associated with filtrations. \par The first main result implies that if a maximal subalgebra $L\sb 0$ of L has solvable quotients of dimension $\ge 2$, then every nilpotent ideal of $L\sb 0$ acts nilpotently on L. It is shown that if L contains a solvable maximal subalgebra, then L is of type $A\sb 1$ or $W\sb 1$. In the final part of the article it is shown that certain Z-graded finite- dimensional simple Lie algebras either are classical or the difference between the number of nonzero positive and negative homogeneous components is large.
[G.Brown]

MSC 2000:: *17B50 Modular Lie algebras
17B70 Graded Lie algebras

Keywords: graded Lie algebras; prime characteristic; filtrations; maximal subalgebra; simple Lie algebras

Cited in: Zbl 1041.17023 Zbl 0781.17010 Zbl 0743.17022

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