$\delta$-superderivations of KKM Double

TL;DR

This paper classifies $\delta$-superderivations of the simple Jordan superalgebra KKM Double, revealing their relationship with algebraic properties and providing new examples of non-trivial derivations.

Contribution

It describes $\delta$-superderivations of KKM Double and constructs new non-trivial 1/2-derivations of Jordan superalgebras of vector type.

Findings

Relationship between non-trivial $\delta$-derivations and algebraic properties.

Classification of $\delta$-superderivations for KKM Double.

New examples of non-trivial 1/2-derivations.

Abstract

We described $\delta$-derivations and $\delta$-superderivations of simple Jordan superalgebra <<KKM Double>> (also known as superalgebra of Jordan brackets) and unital simple finite-dimensional Jordan superalgebras over algebraic closed fields with characteristic $p\neq2$. As a consequence, we received relationship between non-trivial $\delta$-derivations and specialty of simple superalgebra <<KKM Double>>. We constructed new examples of non-trivial 1/2-derivations of Jordan superalgebras of vector type.