On ID*-superderivations of Lie superalgebras

Let L be a Lie superalgebra over a field of characteristic different from 2, 3 and write ID*(L) for the Lie superalgebra consisting of superderivations mapping L to L-2 and the central elements to zero. In this paper we first give an upper bound for the superdimension of ID*(L) by means of linear vector space decompositions. Then we characterize the ID*-superderivation superalgebras for the nilpotent Lie superalgebras of class 2 and the model filiform Lie superalgebras by methods of block matrices.