DEFORMED LIE-POISSON STRUCTURES FOR QUANTIZED GROUPS

The geometrical description of deformation quantization based on quant um duality principle makes it possible to introduce deformed Lie-Poiss on structure. It serves as a natural analogue of classical Lie bialgeb ra for the case when the initial object is a quantized group. The expl icit realization of the deformed Lie-Poisson structure is a difficult problem. We study the special case of such constructions characterized by quite a simple form of tangent vector fields. In this case 4 Lie c ompositions define 2 deformations of the first order and 4 Lie bialgeb ras and give rise to 2 families of deformed Lie-Poisson structures. Th e explicit example is studied.