Abstract
The geometrical description of deformation quantization based on quantum duality principle makes it possible to introduce deformed Lie-Poisson structure. It serves as a natural analogue of classical Lie bialgebra for the case when the initial object is a quantized group. The explicit 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 compositions define 2 deformations of the first order and 4 Lie bialgebras and give rise to 2 families of deformed Lie-Poisson structures. The explicit example is studied.
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Lyakhovsky, V., Mirolubov, A. Deformed Lie-Poisson structures for quantized groups. Czechoslovak Journal of Physics 47, 63–70 (1997). https://doi.org/10.1023/A:1021496128802
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DOI: https://doi.org/10.1023/A:1021496128802