The classification of the simple modular Lie algebras. II: The toral structure
This is the second in a series of papers on the classification of the simple modular Lie algebras. Three others have appeared in Ann. Math., II. Ser. [I: 130, 643-677 (1989; Zbl 0699.17016); III: 133, 577-604 (1991; Zbl 0736.17021); IV: 178, 1-59 (1993)]. The special case of the classification in which the algebras are restricted was carried out by \textit{R. E. Block} and \textit{R. L. Wilson} [J. Algebra 114, 115-259 (1988; Zbl 0644.17008)] and influences the approach taken for the more general investigation. Let \(L\) be a simple Lie algebra over an algebraically closed field of characteristic \(p>7\) and \(T\) an optimal torus in some \(p\)-envelope \(L_ p\). The 2-sections of \(L\) with respect to \(T\) were described in the first paper of this series, but it was necessary to publish some corrections to these results in this second paper. After doing so, the author proceeds in a case-by-case investigation to determine the action of \(T\) on these 2-sections. Other significant results include new noncomputational proofs determining the conjugacy classes of the tori in \(W(n;\mathbf{1})\) and of the Cartan subalgebras of \(W(1;{\mathbf n})\).
scientific article; zbMATH DE number 165845
scientific article