English

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