Simple Lie algebras of small characteristic VI. Completion of the classification
Representation Theory
2008-08-11 v3 Rings and Algebras
Abstract
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.
Keywords
Cite
@article{arxiv.0711.2899,
title = {Simple Lie algebras of small characteristic VI. Completion of the classification},
author = {Alexander Premet and Helmut Strade},
journal= {arXiv preprint arXiv:0711.2899},
year = {2008}
}
Comments
Many typos corrected and introduction extended; the new version is accepted for publication