Triangular Poisson structures on Lie groups and symplectic reduction

Details Triangular Poisson structures on Lie groups and symplectic reduction Triangular Poisson structures on Lie groups and symplectic reduction

2004-12-03

arxiv.org/abs/math/0412082v1

Mathematics

Symplectic Geometry

12 pages, AMS-Latex

Scientific paper

We show that each triangular Poisson Lie group can be decomposed into Poisson submanifolds each of which is a quotient of a symplectic manifold. The Marsden-Weinstein-Meyer symplectic reduction technique is then used to give a complete description of the symplectic foliation of all triangular Poisson structures on Lie groups. The results are illustrated in detail for the generalized Jordanian Poisson structures on SL(n).

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