Ko Mold Lie Algebra

Lie superalgebras have seen a remarkable evolution both in mathematics and physics.And the research field of Lie superalgebras is still active because of their important application in physics.The study of Lie superalgebras over a field of characteristic zero has obtained plentiful results.But that is not the case with modular Lie superalgebras .In 1977,Kac V.G. gave the classification of Lie superalgebras over a characteristic zero.But it isn't the case of modular Lie superalgebras. In 1997,Pro Zhang constructed four class of simple finite dimension Cartan-type modular Lie superalgebras:W,S,H,K.And gave a supposition of the classification of modular Lie superalgebras of finite dimension.Now someone found the fifth class simple finite dimension Cartan-type modular Lie superalgebras HO.Derivation algebras play an important role in the research of Lie algebras and Lie superalgebras.Until 1988,the derivation algebras of finite dimensional modular Lie algebras of Cartan-type had been researched.In this paper we give a new class of finite-dimensional simple Lie superalgebras over a field of prime characteristic^ > 3) :KO: then obtain these results:Theoreml KO(n, n + 1, t) is simple Lie superalgebras. Theorem2 KO(n, n+1, t) haven't undegenerate associative forms.Theorems dimKO(n,n + l,t) = 2n+1 -pm, there m = ?f,.(=iTheorem4...