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On subalgebras of simple Lie algebras of characteristic $ p>0$


Author: B. Weisfeiler
Journal: Trans. Amer. Math. Soc. 286 (1984), 471-503
MSC: Primary 17B50
DOI: https://doi.org/10.1090/S0002-9947-1984-0760972-8
MathSciNet review: 760972
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Abstract: The main results of the paper are Theorems I.5.1, II.1.3 and III.2.1. Theorem I.5.1 states that if a maximal subalgebra $ M$ of a simple finite-dimensional Lie algebra $ G$ has solvable quotients of dimension $ \geqslant 2$, then every nilpotent element of $ H$ acts nilpotently on $ G$. Theorem II.1.3 states that if such a simple Lie algebra $ G$ contains a maximal subalgebra which is solvable, then $ G$ is Zassenbaus-Witt algebra. Theorem III.2.1 states that certain $ {\mathbf{Z}}$-graded finite-dimensional simple Lie algebras are either classical or the difference between the number of nonzero positive and negative homogeneous components is large.


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DOI: https://doi.org/10.1090/S0002-9947-1984-0760972-8
Article copyright: © Copyright 1984 American Mathematical Society

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