Jordan Derivations of some extension algebras

TL;DR

This paper investigates Jordan derivations on dual extension and generalized one-point extension algebras, showing that under certain conditions, these derivations are actually derivations or sums of derivations and anti-derivations.

Contribution

It proves that all Jordan derivations on dual extension algebras are derivations and characterizes Jordan derivations on generalized one-point extension algebras.

Findings

Every Jordan derivation of dual extension algebras is a derivation.

Jordan generalized derivations are generalized derivations.

Jordan derivations on certain extension algebras decompose into derivations and anti-derivations.

Abstract

In this paper, we mainly study Jordan derivations of dual extension algebras and those of generalized one-point extension algebras. It is shown that every Jordan derivation of dual extension algebras is a derivation. As applications, we obtain that every Jordan generalized derivation and every generalized Jordan derivation on dual extension algebras are both generalized derivations. For generalized one-point extension algebras, it is proved that under certain conditions, each Jordan derivation of them is the sum of a derivation and an anti-derivation.