LEIBNIZ AND LIE-ALGEBRA STRUCTURES FOR NAMBU ALGEBRA

We canonically associate a Leibniz algebra with every Nambu algebra. W e show how various homological and cohomological complexes for a Nambu algebra can be naturally obtained from its structure as a module over the Leibniz algebra. We also present a generalization of a classical Lie-Berezin construction for Nambu algebras and extend these results f or Nambu superalgebras.