Higher ξ-lie Derivable Maps On Triangular Algebras By Jordan Zero Products

In this paper,using the method of algebraic decomposition,we mainly study the problem of higher ξ-Lie derivable maps on triangular algebras by Jordan zero products.The details are as follows:In Chapter 1,some common notions,definitions（for example.triangular algebra,higher derivations,higher ξ-Lie derivable maps and so on）and a well-known theorem involved in the article are given.In Chapter 2,we discuss higher ξ-Lie derivable maps on triangular algebras by Jordan zero products.It is shown that every higher ξ-Lie derivable map on a triangular algebra u by Jordan zero products with ξ≠±1 is a higher derivation;every higher-1-Lie derivable map {φn｝n∈N on a triangular algebra u by Jordan zero products has the form U→Ψn（U）+UTn-TnU+φn（I）U,where Tn ∈ u,{Ψn｝n∈N is a higher derivation on u;every higher 1-Lie derivable map {φn｝n∈N on a triangular algebra u by Jordan zero products has the form u→Ψn（U）+UTn-TnU+hn（U）,where Tn ∈ u,{Ψn}n∈N is a higher derivation on u and every map {hn}n∈N from U into its center is zero on the commutators whose Jordan products are zero.As an application,we also characterize higher ξ-Lie derivable maps on nontrivial nest algebras by Jordan zero products.