  The polynomial deformations of the Witten extensions of the U(su(2)) and
U(osp(1,2)) algebras are three generator algebras with normal ordering,
admitting a two generator subalgebra. The modules and the representations of
these algebras are based on the construction of Verma modules, which are
quotient modules, generated by ideals of the original algebra. This
construction unifies a large number of the known algebras under the same
scheme. The finite dimensional representations show new features such as the
multiplicity of representations of the same dimensionality, or the existence of
finite dimensional representations only for some dimensions.
