Product Zero Derivations on Strictly Upper Triangular Matrix Lie Algebras

Let F be a field,n≥3,N(n,F) the strictly upper triangular matrix Lie algebra consisting of the n×n strictly upper triangular matrices and with the bracket operation [x,y] = xy yx.A linear map on N(n,F) is said to be a product zero derivation if [(x),y] + [x,(y)] = 0 whenever [x,y] = 0,x,y∈N(n,F).In this paper,we prove that a linear map on N(n,F) is a product zero derivation if and only if is a sum of an inner derivation,a diagonal derivation,an extremal product zero derivation,a central product zero derivation and a scalar multiplication map on N(n,