Triangular Poisson structures on Lie groups and symplectic reduction
- Resource Type
- Working Paper
- Authors
- Hodges, Timothy J.; Yakimov, Milen
- Source
- Subject
- Mathematics - Symplectic Geometry
Mathematics - Quantum Algebra
53D20
17B62, 53D17, 17B37
- Language
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).
Comment: 12 pages, AMS-Latex