Higher-order Triangular Lie Algebra Can Guide Maps

In this paper, using induction, we detailedly study higher Lie derivable maps at zero point and higher Lie derivable maps at an idempotent on triangular algebras.In Chapter1, some common symbols, definitions and some well-known theorem are given.In Chapter2, we discuss the structure of higher Lie derivable maps at zero point on triangular algebras, and prove that every higher Lie derivable map at zero point is the sum of a higher derivation and a center-valued map.In Chapter3, we study higher Lie derivable maps at an idempotent on triangular algebras, and prove that every higher Lie derivable map at an idempotent is the sum of a higher derivation and a center-valued map.