| Using Krichever-Phong's universal formula, we show that a multiplicative representation linearizes Sklyanian quadratic brackets for a multi-pole Lax function with a spectral parameter. The spectral parameter can be either rational or elliptic. As a by-product, we obtain an extension of a Sklyanin algebra in the elliptic case. We discuss applications of these results to isospectral and isomonodromic equations with discrete time. Krichever-Phong's formula provides a hierarchy of symplectic structures, and we show that there exists a non-trivial cubic bracket in Sklyanin's case. Also, we consider a generalization of the universal formula to variable base curves (suggested in [22]) in the simplest possible case of a rational base curve with moving marked points. |
