Simple Lie algebras of small characteristic VI. Completion of the classification

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/166675Let L be a finite-dimensional simple Lie algebra over an algebraically closed field of F characteristic p>3. We prove that if the p-envelope of L in the derivation algebra of L contains nonstandard tori of maximal dimension, then p=5 and L is isomorphic to one of the Melikian algebras. Together with our earlier results this implies that any finite-dimensional simple Lie algebra over F is of classical, Cartan or Melikian type.Many typos corrected and introduction extended; the new version is accepted for publicationRepresentation TheoryRings and Algebras17B20; 17B50Simple Lie algebras of small characteristic VI. Completion of the classificationtext