$\delta$-Superderivations of semisimple finite-dimensional Jordan superalgebras

Abstract

In the paper, a complete description of the $\delta$-derivations and the $\delta$-superderivations of semisimple finite-dimensional Jordan superalgebras over an algebraically closed field of characteristic $p\ne 2$ is given. In particular, new examples of nontrivial $\frac{1}{2}$-derivations and odd $\frac{1}{2}$-superderivations are given that are not operators of right multiplication by an element of the superalgebra.

arXiv commentCorrected version verified in Lean

References in corpus (3)

• On $\delta$-derivations of Lie algebras and superalgebras
• $\delta$-superderivations of simple finite-dimensional Jordan and Lie superalgebras
• $\delta$-derivations of simple finite-dimensional Jordan superalgebras

Cited by in corpus (14)

• Generalized derivations of (color) n-ary algebras
• Transposed Poisson structures on Block Lie algebras and superalgebras
• Transposed Poisson structures on Witt type algebras
• Degenerations of Jordan Superalgebras
• Transposed Poisson structures on Galilean and solvable Lie algebras
• Generalized derivations of multiplicative $n$-ary Hom-$\Omega$ color algebras
• Conservative algebras of 2-dimensional algebras
• Alternative algebras admitting derivations with invertible values and invertible derivations
• $\delta$-derivations of n-ary algebras
• Transposed Poisson structures
• $\delta$-derivations of semisimple finite-dimensional structurable algebras
• The structure of simple noncommutative Jordan superalgebras
• $n$-Ary generalized Lie-type color algebras admitting a quasi-multiplicative basis
• $\frac{1}{2}$-derivations of Lie algebras and transposed Poisson algebras