  In this paper, we study weak bialgebras and weak Hopf algebras. These
algebras form a class wider than bialgebras respectively Hopf algebras. The
main results of this paper are Kaplansky's constructions type which lead to
weak bialgebras or weak Hopf algebras starting from a regular algebra or a
bialgebra. Also we provide a classification of 2-dimensional and 3-dimensional
weak bialgebras and weak Hopf algebras. We determine then the stabilizer group
and the representative of these classes, the action being that of the linear
group.
