  In this article we continue the classical analysis of the symmetry algebra
underlying the integrability of the spectrum in the AdS_5/CFT_4 and in the
Hubbard model. We extend the construction of the quasi-triangular Lie bialgebra
gl(2|2) by contraction and reduction studied in the earlier work to the case of
the affine algebra sl(2)^(1) times d(2,1;alpha)^(1). The reduced affine
derivation naturally measures the deviation of the classical r-matrix from the
difference form. Moreover, it implements a Lorentz boost symmetry, originally
suggested to be related to a q-deformed 2D Poincare algebra. We also discuss
the classical double construction for the bialgebra of interest and comment on
the representation of the affine structure.
