RESIDUAL FINITENESS OF COLOR LIE-SUPERALGEBRAS

A (color) Lie superalgebra L over a field K of characteristic not-equal 2, 3 is called residually finite if any of its nonzero elements remains nonzero in a finite-dimensional homomorphic image of L. In what follows we are looking for necessary and sufficient conditions under which all finitely generated Lie superalgebras satisfying a fixed system of identical relations are residually finite. In the case char K = 0 we show that a variety V satisfies this property if and only if V does not contain atl center-by-metabelian algebras and every finitely generated algebra of V has nilpotent commutator subalgebra.