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Mohammad Ashraf, Nazia Parveen and Bilal Ahmad Wani

Abstract

Let be the triangular algebra consisting of unital algebras A and B over a commutative ring R with identity 1 and M be a unital (A; B)-bimodule. An additive subgroup L of A is said to be a Lie ideal of A if [L;A] ⊆ L. A non-central square closed Lie ideal L of A is known as an admissible Lie ideal. The main result of the present paper states that under certain restrictions on A, every generalized Jordan triple higher derivation of L into A is a generalized higher derivation of L into A.

Open access

Mohammad Ashraf, Shakir Ali and Bilal Ahmad Wani

Abstract

Let ℌ be an in finite-dimensional complex Hilbert space and A be a standard operator algebra on ℌ which is closed under the adjoint operation. It is shown that every nonlinear *-Lie higher derivation D = {δn}gn∈N of A is automatically an additive higher derivation on A. Moreover, D = {δn}gn∈N is an inner *-higher derivation.