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.
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