Jordan Higher Derivations on Trivial Extension Algebras

Abstract

Abstract. We first give the constructions of (Jordan) higher derivations on a trivial extension algebra and then we provide some sufficient conditions under which a Jordan higher derivation on a trivial extension algebra is a higher derivation. We then proceed to the trivial generalized matrix algebras as a special trivial extension algebra. As an application we characterize the construction of Jordan higher derivations on a triangular algebra. We also provide some illuminating examples of Jordan higher derivations on certain trivial extension algebras which are not higher derivations.

Lie higher derivations on triangular algebras revisited

“…Many authors have studied the problem for various algebras; see [5,6,7,8,15,16,17,21,22,23] and references therein.…”

A Note on Jordan Derivations of Trivial Generalized Matrix Algebras

“…R. Ebrahimi Vishki et al conjectured in [1] that if every Jordan higher derivation on a trivial generalized matrix algebra G = (A, M, N, B) is a higher derivation, then either M = 0 or N = 0. In this note, we will give a class of counter examples.…”