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 finitedimensional Lie superalgebras and Jordan superalgebras over an algebraically closed field of characteristic 0. We give a complete description of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \frac{1}{2} $$\end{document}-derivations for Cartantype 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.