Linear $r$-Matrix Algebra for Systems Separable\\ in Parabolic Coordinates

Details Linear $r$-Matrix Algebra for Systems Separable\\ in Parabolic Coordinates Linear $r$-Matrix Algebra for Systems Separable\\ in Parabolic Coordinates

1993-08-30

arxiv.org/abs/hep-th/9308143v1

Phys.Lett. A 180 (1993) 208

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, LaTeX. Submitted to Phys.Lett.A

Scientific paper

10.1016/0375-9601(93)90697-X

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 $2\times 2$ matrices for the whole hierarchy, we construct
the associated linear $r$-matrix algebra with the $r$-matrix dependent on the
dynamical variables. A dynamical Yang-Baxter equation is discussed.

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