The Poisson Transform for Split Reductive Symmetric Spaces.
H. Thorleifsson (1996)
Mathematica Scandinavica
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H. Thorleifsson (1996)
Mathematica Scandinavica
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Eugene Karolinsky (2000)
Banach Center Publications
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Let G be a complex reductive connected algebraic group equipped with the Sklyanin bracket. A classification of Poisson homogeneous G-spaces with connected isotropy subgroups is given. This result is based on Drinfeld's correspondence between Poisson homogeneous G-spaces and Lagrangian subalgebras in the double D𝖌 (here 𝖌 = Lie G). A geometric interpretation of some Poisson homogeneous G-spaces is also proposed.
Sam Evens, Jiang-Hua Lu (2001)
Annales scientifiques de l'École Normale Supérieure
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P.L. Lions, B. Perthame (1991)
Inventiones mathematicae
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Vaisman, I. (1999)
Acta Mathematica Universitatis Comenianae. New Series
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Dimitri Gurevich, Pavel Saponov (2011)
Banach Center Publications
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We consider Poisson pencils, each generated by a linear Poisson-Lie bracket and a quadratic Poisson bracket corresponding to a so-called Reflection Equation Algebra. We show that any bracket from such a Poisson pencil (and consequently, the whole pencil) can be restricted to any generic leaf of the Poisson-Lie bracket. We realize a quantization of these Poisson pencils (restricted or not) in the framework of braided affine geometry. Also, we introduce super-analogs of all these Poisson...
Adam Korányi (1976)
Inventiones mathematicae
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Jan Vysoký, Ladislav Hlavatý (2012)
Archivum Mathematicum
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Poisson sigma models represent an interesting use of Poisson manifolds for the construction of a classical field theory. Their definition in the language of fibre bundles is shown and the corresponding field equations are derived using a coordinate independent variational principle. The elegant form of equations of motion for so called Poisson-Lie groups is derived. Construction of the Poisson-Lie group corresponding to a given Lie bialgebra is widely known only for coboundary Lie bialgebras....