Nonlinear Jordan derivable mappings of generalized matrix algebras by Lie product square-zero elements (Q2052059)

Summary: The aim of the paper is to give a description of nonlinear Jordan derivable mappings of a certain class of generalized matrix algebras by Lie product square-zero elements. We prove that under certain conditions, a nonlinear Jordan derivable mapping \(\Delta\) of a generalized matrix algebra by Lie product square-zero elements is a sum of an additive derivation \(\delta\) and an additive antiderivation \(f\). Moreover, \(\delta\) and \(f\) are uniquely determined.