Classification of osp(2|2) Lie super-bialgebras

The need of classification of Lie bialgebras [1] comes from their close relation with q-deformations of universal enveloping algebras in the Drinfeld sense. To each such deformation there corresponds a Lie bialgebra which may be recovered from the first order of the deformation of the coproduct. It has also been shown [4] that each Lie bialgebra admits quantization. So the classification of Lie bialgebras can be seen as the first step in classification of quantum algebras. Along these lines several efforts (see e.g. [6, 7, 8, 9] to list only a few) have been undertaken in order to classify those Hopf algebras which can be of importance in physics. The Osp(2|2) super-group is a subgroup of two-dimensional N = 2 superconformal symmetry which plays an important role in string theory. In [10] the correlation functions of N = 2 super-conformal field theory were found by using the Osp(2|2) symmetry group. Lattice models based on Uq(osp(2|2)) symmetry were constructed in [11], where also new solutions to the graded Yang-Baxter equation were found.