Superderivations for a Family of Lie Superalgebras of Special Type

Abstract

By means of generators, superderivations are completely determined for a family of Lie superalgebras of Special type, the tensor products of the exterior algebras and the finite-dimensional Special Lie algebras over a field of characteristic $p > 3$. In particular, the structure of the outer superderivation algebra is concretely formulated and the dimension of the first cohomology group is given.