Simple Lie Algebras of Small Characteristic: I. Sandwich Elements Original Research Article

LetLbe a finite dimensional simple Lie algebra over an algebraically closed field of characteristicp > 3 of absolute toral rank 2, andTa 2-dimensional torus in the semisimplep-envelope ofL. It is proved thatLis either classical or a Block algebra or contains sandwich elements which are homogeneous with respect toTor a conjugate toT. In addition, several dimension estimates are given.