$\delta$-superderivations of simple finite-dimensional Jordan and Lie superalgebras

Abstract

We introduce the concept of a $\delta$-superderivation of a superalgebra. $\delta$-Derivations of Cartan-type Lie superalgebras are treated, as well as $\delta$-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 $\delta$-(super)derivations are missing on the given classes of superalgebras, and as a consequence, $\delta$-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 $\delta$-derivations of unital flexible and semisimple finite-dimensional Jordan algebras over a field of characteristic not 2.

14 pages

References in corpus (2)

• $\delta$-derivations of simple Jordan algebras and superalgebras
• $\delta$-derivations of classical Lie superalgebras

Cited by in corpus (13)

• Generalized derivations of (color) n-ary algebras
• A characterization of nilpotent nonassociative algebras by invertible Leibniz-derivations
• $\delta$-superderivations of semisimple Jordan superalgebras
• Generalized derivations of multiplicative $n$-ary Hom-$\Omega$ color algebras
• Conservative algebras of 2-dimensional algebras
• (n+1)-Ary derivations os semisimple Filippov algebras
• 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
• $\delta$-superderivations of KKM Double
• Jordan algebras admitting derivations with invertible values
• $\frac{1}{2}$-derivations of Lie algebras and transposed Poisson algebras