  A class of representations of a Lie superalgebra (over a commutative
superring) in its symmetric algebra is studied. As an application we get a
direct and natural proof of a strong form of the Poincare'-Birkhoff-Witt
theorem, extending this theorem to a class of nilpotent Lie superalgebras.
Other applications are presented. Our results are new already for Lie algebras.
