Poisson Lie groups and Hamiltonian theory of the Yang-Baxter maps
Abstract
We show how the theory of Poisson Lie groups can be used to establish the Poisson properties of the Yang-Baxter maps and related transfer dynamics. As an example we present the Hamiltonian structure for the matrix KdV soliton interaction.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- December 2005
- DOI:
- arXiv:
- arXiv:math/0512328
- Bibcode:
- 2005math.....12328R
- Keywords:
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- Mathematics - Quantum Algebra;
- Mathematics - Dynamical Systems;
- 81R12;
- 37K05
- E-Print:
- 9 pages. Slightly revised version, two references added