CLASSIFICATION OF FOUR-DIMENSIONAL REAL LIE BIALGEBRAS OF SYMPLECTIC TYPE AND THEIR POISSON-LIE GROUPS

摘要

We classify all four-dimensional real Lie bialgebras of symplectic type and obtain the classical r-matrices for these Lie bialgebras and Poisson structures on all the associated four-dimensional Poisson-Lie groups. We obtain some new integrable models where a Poisson-Lie group plays the role of the phase space and its dual Lie group plays the role of the symmetry group of the system.