论文信息 - Classification of simple Lie algebras over algebraically closed fields of prime characteristic

Classification of simple Lie algebras over algebraically closed fields of prime characteristic

We announce here a result which completes the classification of the finite-dimensional simple Lie algebras over an algebraically closed field F of characteristic p > 7, showing that these algebras are all of classical or Cartan type. This verifies the Generalized Kostrikin-Safareviö Conjecture [Kos-70, Kac-74]. Many authors have contributed to the solution of this problem. For a discussion of work before 1986 see [Wil-87]. More recent work is cited in §1. Let F be an algebraically closed field of characteristic p > 1 and L be a finite-dimensional semisimple Lie algebra over F. We identify L with adL, the subalgebra of inner derivations of L and write Z for the restricted subalgebra of DerL (the algebra of derivations of L) generated by L. A torus T in L is a restricted subalgebra such that for every element x e T, adx is a semisimple linear transformation on L. Let ^(L) denote the set of tori contained in L. The (absolute) toral rank of L is

Robert L. Wilson | H. Strade

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