  The question of whether or not any zero torsion linear map on a non abelian
real Lie algebra g is necessarily an extension of some CR-structure is
considered and answered in the negative. Two examples are provided, one in the
negative and one in the positive.In both cases, the computation up to
equivalence of all zero torsion linear maps on g is used for an explicit
description of the equivalence classes of integrable complex structures on the
direct product g x g.
