On subalgebras of simple Lie algebras of characteristic

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 of a simple finite-dimensional Lie algebra has solvable quotients of dimension , then every nilpotent element of acts nilpotently on . Theorem II.1.3 states that if such a simple Lie algebra contains a maximal subalgebra which is solvable, then is Zassenbaus-Witt algebra. Theorem III.2.1 states that certain -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