$\delta$-superderivations of semisimple Jordan superalgebras

TL;DR

This paper classifies and constructs examples of $elta$-derivations and superderivations in semisimple Jordan superalgebras over algebraically closed fields with characteristic not 2, including new examples for Zelmanov's superalgebra.

Contribution

It provides a comprehensive description of $elta$-derivations and superderivations for simple and semisimple Jordan superalgebras, introducing new examples for specific superalgebras.

Findings

Classified $elta$-derivations and superderivations in semisimple Jordan superalgebras.

Constructed new examples of 1/2-derivations and 1/2-superderivations.

Extended understanding of derivations in Jordan superalgebra structures.

Abstract

We described $\delta$-derivations and $\delta$-superderivations of simple and semisimple finite-dimensional Jordan superalgebras over algebraic closed fields with characteristic $p\neq2$. We constructed new examples of 1/2-derivations and 1/2-superderivations of simple Zelmanov's superalgebra $V_{1/2}(Z,D).$