＜正＞ Over an algebraically closed field F of characteristic p＞3,classes of Lie algebras =（n,m,,G）（m＞0）,=（n,m,r,G）（n+20（modp））and =（n,m,,G）(（n+2≡0（modp））are constructed,where n,m are non-negative numbers,=（S0+1,s1+1,…,sn+1,t1+1,…,tn+1）is a（2n+1）tuple of positive numbers and G is a subgroup of the additivegroup of F., and are shown to be all simple Lie algebras with dimensions pN-2,pNand PN-1 respectively,whereTheir derivation algebras are determined.It is shown that they are of generalized Cartantype K when m=0 and of generalized Cartan type H when m＞0.It is then determined that and are new simple Lie algebras if n＞0.Conditions of isomorphism are obtained.Anda special graded algebra structure,the K-like gradation,is discussed.
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