The classification of the simple modular Lie algebras. V: Algebras with Hamiltonian two-sections (Q1341257)

The classification of simple Lie algebras over algebraically closed fields of characteristic \(p>7\), whose completion was announced by the author and \textit{R. L. Wilson} [Bull. Am. Math. Soc., New Ser. 24, 357-362 (1991; Zbl 0725.17023)], was accomplished by dividing the investigation into cases defined by differing properties of one-sections and two- sections with respect to a torus of maximal absolute toral rank. This is the paper that considers the case in which there exists a nonclassical root and a two-section which has core \(H(2; 1;\Phi (\tau) )^{(1)}\). The conclusion that such an algebra is of Cartan type is achieved by showing the existence of a certain subalgebra satisfying the hypotheses of a recognition theorem of \textit{R. L. Wilson} [J. Algebra 40, 418-465 (1976; Zbl 0355.17012)].