Symplectic leaves of complex reductive Poisson-Lie groups (Q1847919)

In the early 1980s, Belavin and Drinfeld classified all non-skew-symmetric \(r\)-matrices on complex simple Lie algebras. Their classification yields a description of all factorizable Lie bialgebra structures on complex reductive Lie algebras. In the present paper, the general classification of the symplectic leaves of the corresponding Poisson-Lie groups is worked out. A formula for the dimensions of the above symplectic leaves is also given.