Classical Yang-Baxter equation and left invariant affine geometry on Lie groups

Let G be a Lie group, T*G=Lie(G)*xG its cotangent bundle considered as a Lie group, where G acts on Lie(G)* via the coadjoint action. Each solution r of the Classical Yang Baxter Equation on G, corresponds to a connected Lie subgroup H of T*G such that Lie(H) is a Lagrangian graph in Lie(G)+Lie(G)* and H carries a left invariant affine structure. If r is invertible, the Poisson Lie tensor pi given by r on G is polynomial of degree at most 2 and every double Lie group of (G,pi) is endowed with an affine and a complex structures del and J, both left invariant and given by r, such that delJ=0.