Nonlinear Lie triple higher derivation on triangular algebras

Generalized Higher Derivations on Lie Ideals of Triangular Algebras

“…Moafian and Ebrahimi Vishki [16] given the structure of Lie higher derivations on triangular algebras by the entries of matrices and obtained a similar conclusion as shown by Li and Shen [13]. Ashraf and Jabeen [3] studied nonlinear Lie triple higher derivations on triangular algebras and proved that under certain conditions every nonlinear Lie triple higher derivation on a triangular algebra is proper. Recently, Ashraf et al [1] gave a description of Lie triple derivations of arbitrary triangular algebras.…”

“…Lie triple (higher-) derivations in different background have been studied extensively (see [1][2][3]24] and references therein). In 2012, Li and Shen [13] showed that under certain assumptions every Lie higher derivation and Lie triple derivation on a triangular algebra are proper, respectively.…”

Lie triple derivation and Lie bi-derivation on quaternion rings

“…Hence, working on Lie triple derivations allows treating both the major classes, viz., Jordan and Lie derivations at the same time. Previously, numerous authors have contributed significantly to the related concerns (see [1,2,4,5,9,10,13,14,17,18]) for the Lie triple derivation. In fact, usually the researchers obtained that a Lie triple derivation on a unital algebra is proper, meaning it could be represented as the sum of additive derivation and linear functional that vanishes on all Lie triple products.…”