  We show that each triangular Poisson Lie group can be decomposed into Poisson
submanifolds each of which is a quotient of a symplectic manifold. The
Marsden-Weinstein-Meyer symplectic reduction technique is then used to give a
complete description of the symplectic foliation of all triangular Poisson
structures on Lie groups. The results are illustrated in detail for the
generalized Jordanian Poisson structures on SL(n).
