Classical Lie bialgebras for AdS/CFT integrability by contraction and reduction

Integrability of the one-dimensional Hubbard model and factorised scattering problem encountered on worldsheet AdS strings can be expressed in terms a peculiar quantum algebra. In this article, we derive classical limit these algebraic integrable structures based established results for exceptional simple Lie superalgebra d(2,1;epsilon) along with standard sl(2) which form supersymmetric isometries 3D space. The two major steps construction consist contraction to Poincar\'e certain reduction deformation u(2|2) superalgebra. We apply structure obtain desired bialgebras suitable r-matrices rational trigonometric kind. illustrate our findings representations on-shell fields flat