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).

The concepts of derivation and centroid for Lie–Yamaguti algebras are generalized in this paper. A quasi-derivation a LY-algebra can be embedded as larger LY-algebra. relationship between quasi-derivations robustness has been studied.