Poisson structures on double Lie groups

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.

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Bibliographic Details
Published inJournal 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
LanguageEnglish
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
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Summary: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.
ISSN:0393-0440
1879-1662
DOI:10.1016/S0393-0440(97)00063-6