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Using Krichever-Phong's universal formula, we show that a multiplicativerepresentation linearizes Sklyanin quadratic brackets for a multi-pole Laxfunction with a spectral parameter. The spectral parameter can be eitherrational or elliptic. As a by-product, we obtain an extension of a Sklyaninalgebra in the elliptic case. Krichever-Phong's formula provides a hierarchy ofsymplectic structures, and we show that there exists a non-trivial cubicbracket in Sklyanin's case.

Quadratic algebras and integrable chains