Generalized derivations of (color) n-ary algebras

Abstract

We generalize the results of Leger and Luks about generalized derivations of Lie algebras to the case of color $n$-ary $\Omega$-algebras. Particularly, we prove some properties of generalized derivations of color $n$-ary algebras; prove that a quasiderivation algebra of a color $n$-ary $\Omega$-algebra can be embedded into the derivation algebra of a larger color $n$-ary $\Omega$-algebra, and describe (anti)commutative $n$-ary algebras satisfying the condition $QDer=End.$

References in corpus (1)

• Generalized Derivations of Hom-Lie Superalgebras

Cited by in corpus (11)

• A characterization of nilpotent nonassociative algebras by invertible Leibniz-derivations
• Higher Derivations of Finitary Incidence Algebras
• Generalized derivations of multiplicative $n$-ary Hom-$\Omega$ color algebras
• BiHom-Lie colour algebras structures
• Generalized Derivations and Rota-Baxter Operators of $n$-ary Hom-Nambu Superalgebras
• $k$-Modules over linear spaces by $n$-linear maps admitting a multiplicative basis
• Split Regular $Hom$-Leibniz Color $3$-Algebras
• $n$-Ary generalized Lie-type color algebras admitting a quasi-multiplicative basis
• Differential Antisymmetric Infinitesimal Bialgebras, Coherent Derivations and Poisson Bialgebras
• $\frac{1}{2}$-derivations of Lie algebras and transposed Poisson algebras
• Double derivations of $n-$Hom-Lie color algebras