Pei Sheng JI(1); Li Hua YUAN(2
Let R be an arbitrary commutative ring with identity.Denote by N(R) the algebra over R consisting of all strictly upper triangular (n+1)×(n+1) matrices over R.We prove that any Lie derivation D of N(R) can be uniquely expressed as D=D_d+D_b+D_c+D_x,where D_d,D_b,D_c,D_x are diagonal,extremal,central and inner Lie derivations,respectively,of N(R) when n(?)3 and R contains 2 as a unit.In the case n=2,we also prove that any Lie derivation D of N(R) can be expressed as a sum of diagonal,extremal and inner Lie derivations.
