Abstract:A new algebraic structure on the orbits of dressing transformations of the quasitriangular Poisson Lie groups is provided. This gives the topological interpretation of the link invariants associated with the Weinstein-Xu classical solutions of the quantum Yang-Baxter equation. Some applications to the three-dimensional topological quantum field theories are discussed.
Keywords: automorphic set, Poisson Lie group, link invariants
AMS Subject Classification: Primary 57M25; Secondary 81R50