$\delta$-derivations of simple Jordan algebras and 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 $\delta$-derivations are shown to be missing for $\delta \ne 0,12,1$, and we give a complete account of $12$-derivations.

13 pages

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• $\delta$-superderivations of semisimple Jordan superalgebras
• Degenerations of Jordan Superalgebras
• Generalized derivations of multiplicative $n$-ary Hom-$\Omega$ color algebras
• Conservative algebras of 2-dimensional algebras
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• Alternative algebras admitting derivations with invertible values and invertible derivations
• δ-derivations of n-ary algebras
• δ-derivations of semisimple structurable algebras
• The structure of simple noncommutative Jordan superalgebras
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