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 $QDer = End.$