The Theory Of The Radical Of Lie Algebras

This thesis constructed the theory of the radical of Lie algebras.And we made use of the knowledge of the radical theory to study the structure of Lie algebras.If r is a property,and also satisfies the following condition:(Rl):Every homomorphic image V of r—lie algebra L is again an r—lie algebra;(R2):Every lie algebra L has a maximum r—ideal R(L);(R3):R(L/R(L))=0.We define the rb property of Lie algebra: L is a rb—Lie algebra if and only if every homomorphic image of L contains non-nilpotent ideal in r(E), then rb is a property.This specific work is in the following:(1)If Witt algebra is a simple Lie algebra,and its Baer-radical rb(L)=0.(2) To any ideal I of Loop algebra L(L), there exists an I1(?)F[l,l-1] which makes I=I1(?)L, L is a simple Lie algebra.(3)The Baer-radical of the twist affine lie algebras is rb(L(L))—Fc.F is a closed domain of characteristic zero algebraic.c is a central element.(4)If L(L):=L(L)+Fc can make a Lie algebra on the base of the following computation:[a+Fc, b+Fc]:=[a, b]0+ψ(a, b)c,ψ(a, b):=(da, b)0, for any a,b∈E L(L), for any ideal I of L(L), there exists I1(?)L(L) which makes I=I1+Fc.