  On the level of Lie algebras, the contraction procedure is a method to create
a new Lie algebra from a given Lie algebra by rescaling generators and letting
the scaling parameter tend to zero. One of the most well-known examples is the
contraction from su(2) to e(2), the Lie algebra of upper-triangular matrices
with zero trace and purely imaginary diagonal. In this paper, we will consider
an extension of this contraction by taking also into consideration the natural
bialgebra structures on these Lie algebras. This will give a bundle of central
extensions of the above Lie algebras with a Lie bialgebroid structure having
transversal component. We consider as well the dual Lie bialgebroid, which is
in a sense easier to understand, and whose integration can be explicitly
presented.
