CONTRACTIONS IN DEFORMED LIE-POISSON STRUCTURES

The geometrical description of deformation quantization based on quant um duality principle makes it possible to introduce deformed Lie-Poiss on structures - natural analogues of classical Lie bialgebras for the case when the initial object is a quantized group. Special types of co ntractions - the so called first order contractions - play the signifi cant role in the explicit realization of deformed Lie-Poisson structur e. Such contractions can be naturally applied to the Drinfeld double. In the case of (u(1) + sl(2))(q) we investigate explicitly the deforme d structures induced by the first order contractions.