Poisson-Lie groups and beyond (Q1356297)

Properties of Poisson-Lie groups and their relation to the ``duality'' of manifolds are studied. The notions of Poisson-Lie groups and their duals are defined. Then it is shown that the quasi-Poisson-Lie groups generalize the Poisson-Lie groups. The semiclassical limit of a quasiquantum group is also studied. Finally, global objects corresponding to the co-Jacobian quasi-algebras are introduced. It is concluded that the properties of quasi-Poisson-Lie groups and the Poisson-Lie-quasigroups, written in parallel, define duality between: (a) the associative multiplication and the Poisson bivector; (b) the quasi-Poisson structure and the quasi-associative multiplication; (c) the global pentagonal and co-pentagonal identities.