1. Poisson structures on double Lie groups
- Author
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Giuseppe Marmo, Peter W. Michor, Janusz Grabowski, Dimitri Alekseevsky, D., Alekseevsky, J., Grabowski, Marmo, Giuseppe, and P. W., Michor
- Subjects
Mathematics - Differential Geometry ,Pure mathematics ,Lie bialgebra ,22E30, 58F05, 70H99 ,Group (mathematics) ,General Physics and Astronomy ,Lie group ,Poisson distribution ,symbols.namesake ,Mathematics::Algebraic Geometry ,Differential Geometry (math.DG) ,Mathematics::Quantum Algebra ,Lie algebra ,symbols ,FOS: Mathematics ,Geometry and Topology ,Mathematical Physics ,Mathematics - Abstract
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., Comment: AmSTeX, 37 pages