  This work addresses some relevant characteristics and properties of
$q$-generalized associative algebras and $q$-generalized dendriform algebras
such as bimodules, matched pairs. We construct for the special case of $q=-1$
an antiassociative algebra with a decomposition into the direct sum of the
underlying vector spaces of another antiassociative algebra and its dual such
that both of them are subalgebras and the natural symmetric bilinear form is
invariant or the natural antisymmetric bilinear form is sympletic. The former
is called a double construction of quadratic antiassociative algebra and the
later is a double construction of sympletic antiassociative algebra which is
interpreted in terms of antidendrifom algebras. We classify the 2-dimensional
antiassociative algebras and thoroughly give some double constructions of
quadratic and sympletic antiassociative algebras.
