Generalized derivations of (color) n-ary algebras

TL;DR

This paper extends the theory of generalized derivations from Lie algebras to color $n$-ary $ ext{Omega}$-algebras, establishing new properties and embedding results for their derivation structures.

Contribution

It generalizes previous results to color $n$-ary $ ext{Omega}$-algebras, providing new insights into their derivation and quasiderivation structures.

Findings

Quasiderivation algebra embeds into derivation algebra of a larger algebra.

Properties of generalized derivations of color $n$-ary algebras are established.

Characterization of (anti)commutative $n$-ary algebras with $QDer = End$.

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 $QDer = End.$