Simple Lie algebras of small characteristic V. The non-Melikian case

Abstract: Let L be a finite-dimensional simple Lie algebra over an algebraically closed field F of characteristic . We prove in this paper that if for every torus T of maximal dimension in the p-envelope of adL in DerL the centralizer of T in adL acts triangulably on L, then L is either classical or of Cartan type. As a consequence we obtain that any finite-dimensional simple Lie algebra over an algebraically closed field of characteristic is either classical or of Cartan type. This settles the last remaining case of the generalized Kostrikin–Shafarevich conjecture (the case where ). [Copyright &y& Elsevier]