The aim of this article is to discuss the n-derivation algebras Lie color algebras. It proved that, if base ring contains 1/n-1, L a perfect algebra with zero center, then every triple derivation derivation, and nDer(L)) an inner derivation.

We study infinite-dimensional analogs of classical Lie superalgebras over an algebraically closed field F zero characteristic. Let I be infinite set. For algebra M_∞ (I) × matrices a ground having finitely many nonzero entries, we consider the related superalgebra gl_∞ (I1, I2) and its commutator sl_∞ for disjoint union nonempty subsets I1 I2 set I; describe derivations I2).