$\delta$-derivations of simple finite-dimensional Jordan superalgebras

Abstract

We describe non-trivial $\delta$-derivations of semisimple finite-dimensional Jordan algebras over an algebraically closed field of characteristic not $2$, and of simple finite-dimensional Jordan superalgebras over an algebraically closed field of characteristic $0$. For these classes of algebras and superalgebras, non-zero non-trivial $\delta$-derivations are shown to be missing for $\delta \notin \{0,\frac{1}{2},1\}$, and we give a complete account of $\frac{1}{2}$-derivations.

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• A characterization of nilpotent nonassociative algebras by invertible Leibniz-derivations
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• Degenerations of Jordan Superalgebras
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• The structure of simple noncommutative Jordan superalgebras
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