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Triangular Poisson structures on Lie groups and symplectic reduction

Timothy J. Hodges·Milen Yakimov
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Abstract

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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Timothy J. Hodges, Milen Yakimov. 2004-12-03. Triangular Poisson structures on Lie groups and symplectic reduction. https://arxiv.org/abs/math/0412082

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