A structural characterization of the simple Lie algebras of generalized Cartan type over fields of prime characteristic

Abstract

Lie algebras of Cartan type over fields of prime characteristic were introduced by Kostrikin and Šafarevič [15]. More general definitions were later given in [12, 13, 16, 23]. In this paper we give a further generalization of the definition of Lie algebra of Cartan type and a structural characterization of the simple finite dimensional Lie algebras of generalized Cartan type over algebraically closed fields.