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$δ$-superderivations of simple finite-dimensional Jordan and Lie superalgebras

We introduce the concept of a $δ$-superderivation of a superalgebra. $δ$-Derivations of Cartan-type Lie superalgebras are treated, as well as $δ$-superderivations of simple finite-dimensional Lie superalgebras and Jordan superalgebras over an algebraically closed field of characteristic 0. We give a complete description of $\{1}{2}$-derivations for Cartan-type Lie superalgebras. It is proved that nontrivial $δ$-(super)derivations are missing on the given classes of superalgebras, and as a consequence, $δ$-superderivations are shown to be trivial on simple finite-dimensional noncommutative Jordan superalgebras of degree at least 2 over an algebraically closed field of characteristic 0. Also we consider $δ$-derivations of unital flexible and semisimple finite-dimensional Jordan algebras over a field of characteristic not 2.