The classification of the simple modular Lie algebras: III. Solution of the classical case

Abstract

We investigate the structure of simple modular Lie algebras over an algebraically closed field of characteristic $p > 7$. If the distinguished subalgebra $Q(L, T)$ with respect to an optimal torus $T$ in some $p$-envelope $L_p$ of $L$ equals $L$, then either $L$ has a two-section of type $H(2; 1; \Phi(\tau))^{(1)}$ or $L$ is of classical type.