Simple Lie algebras of small characteristic VI. Completion of the classification
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Let 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 publication
Many typos corrected and introduction extended; the new version is accepted for publication