Poisson structures on double Lie groups
  Lie bialgebra structures are reviewed and investigated in terms of the double Lie algebra, of Manin- and Gau{\ss}-decompositions. The standard R-matrix in a Manin decomposition then gives rise to several Poisson structures on the correponding double group, which is investigated in great detail. 
D. Alekseevsky, J. Grabowski, G. Marmo, P. W. Michor