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

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 $2\times 2$ 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.

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

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