Triangular Poisson structures on Lie groups and symplectic reduction
Symplectic Geometry
2007-05-23 v1 Quantum Algebra
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).
Keywords
Cite
@article{arxiv.math/0412082,
title = {Triangular Poisson structures on Lie groups and symplectic reduction},
author = {Timothy J. Hodges and Milen Yakimov},
journal= {arXiv preprint arXiv:math/0412082},
year = {2007}
}
Comments
12 pages, AMS-Latex