Linear $r$-Matrix Algebra for Systems Separable\\ in Parabolic Coordinates
High Energy Physics - Theory
2009-10-22 v1
Abstract
We consider a hierarchy of many particle systems on the line with polynomial potentials separable in parabolic coordinates. Using the Lax representation, written in terms of matrices for the whole hierarchy, we construct the associated linear -matrix algebra with the -matrix dependent on the dynamical variables. A dynamical Yang-Baxter equation is discussed.
Cite
@article{arxiv.hep-th/9308143,
title = {Linear $r$-Matrix Algebra for Systems Separable\\ in Parabolic Coordinates},
author = {J. C. Eilbeck and V. Z. Enol'skii and V. B. Kuznetsov and D. V. Leykin},
journal= {arXiv preprint arXiv:hep-th/9308143},
year = {2009}
}
Comments
10 pages, LaTeX. Submitted to Phys.Lett.A