## Contributions to the classification of simple modular Lie algebras

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- by Georgia Benkart, J. Marshall Osborn and Helmut Strade
- Trans. Amer. Math. Soc.
**341**(1994), 227-252 - DOI: https://doi.org/10.1090/S0002-9947-1994-1129435-0
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## Abstract:

We develop results directed towards the problem of classifying the finite-dimensional simple Lie algebras over an algebraically closed field of characteristic $p > 7$. A $1$-section of such a Lie algebra relative to a torus $T$ of maximal absolute toral rank possesses a unique subalgebra maximal with respect to having a composition series with factors which are abelian or classical simple. In this paper we show that the sum $Q$ of those compositionally classical subalgebras is a subalgebra. This extends to the general case a crucial step in the classification by Block and Wilson of the restricted simple Lie algebras. We derive properties of the filtration which can be constructed using $Q$ and obtain structural information about the $1$-sections and $2$-sections of $Q$ relative to $T$. We further classify all those algebras in which $Q$ is solvable.## References

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## Bibliographic Information

- © Copyright 1994 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**341**(1994), 227-252 - MSC: Primary 17B50
- DOI: https://doi.org/10.1090/S0002-9947-1994-1129435-0
- MathSciNet review: 1129435