  We study Lie algebras endowed with an abelian complex structure which admit a
symplectic form compatible with the complex structure. We prove that each of
those Lie algebras is completely determined by a pair (U,H) where U is a
complex commutative associative algebra and H is a sesquilinear hermitian form
on U which verifies certain compatibility conditions with respect to the
associative product on U. The Riemannian and Ricci curvatures of the associated
pseudo-K\"ahler metric are studied and a characterization of those Lie algebras
which are Einstein but not Ricci flat is given. It is seen that all
pseudo-K\"ahler Lie algebras can be inductively described by a certain method
of double extensions applied to the associated complex asssociative commutative
algebras.
