Derivations of infinite-dimensional Lie superalgebras

Abstract

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