The classification of the simple modular Lie algebras: VI. Solving the final case

Strade, H.

doi:10.1090/S0002-9947-98-01770-X

The classification of the simple modular Lie algebras: VI. Solving the final case
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Trans. Amer. Math. Soc. 350 (1998), 2553-2628 Request permission

Abstract:

We investigate the structure of simple Lie algebras $L$ over an algebraically closed field of characteristic $p>7$. Let $T$ denote a torus in the $p$-envelope of $L$ in $\operatorname {Der} L$ of maximal dimension. We classify all $L$ for which every 1-section with respect to every such torus $T$ is solvable. This settles the remaining case of the classification of these algebras.

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