Poisson structures on double Lie groups

• Published in: Journal of geometry and physics Vol. 26; no. 3; pp. 340 - 379
• Main Authors: Alekseevsky, D., Grabowski, J., Marmo, G., Michor, P.W.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.07.1998
• Subjects: Double Lie groups; Gauss decomposition; Lie bialgebras; Manin decomposition; Poisson structures; R-matrices; Poisson structures; Double Lie groups; R-matrices; 16W30; 53C57; Manin decomposition; Differential geometry; 53C15; Gauss decomposition; Lie bialgebras

Lie bialgebra structures are reviewed and investigated in terms of the double Lie algebra, of Manin- and Gauss-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.