On subalgebras of simple Lie algebras of characteristic $p>0$
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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.References
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Additional Information
- © Copyright 1984 American Mathematical Society
- 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