Higher ?-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 ?-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 ?-Lie derivable maps and so on)and a well-known theorem involved in the article are given.In Chapter 2,we discuss higher ?-Lie derivable maps on triangular algebras by Jordan zero products.It is shown that every higher ?-Lie derivable map on a triangular algebra u by Jordan zero products with ??±1 is a higher derivation;every higher-1-Lie derivable map {?n?n?N on a triangular algebra u by Jordan zero products has the form U??n(U)+UTn-TnU+?n(I)U,where Tn ? u,{?n?n?N is a higher derivation on u;every higher 1-Lie derivable map {?n?n?N on a triangular algebra u by Jordan zero products has the form u??n(U)+UTn-TnU+hn(U),where Tn ? u,{?n}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 ?-Lie derivable maps on nontrivial nest algebras by Jordan zero products.