Lie Algebras of CL Type,

The notion of a strongly nilpotent element of a Lie algebra is introduced. According to the existence or nonexistence of nontrivial strongly nilpotent elements, the simple modular Lie algebras are divided into two categories, CA type and CL type, which coincide with Lie algebras of generalized Cartan type and classical type, respectively, when the characteristic is greater than 7. Examples of nonclassical simple Lie algebras of CL type are given which all have affinities to the classical Lie algebras.