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Generalized q-deformed Gelfand-Dickey structures on the group of q-pseudodifference operators

A. L. Pirozerski·M. A. Semenov-Tian-Shansky
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Abstract

We define the q-deformed Gelfand-Dickey bracket on the space of q-pseudodifference symbols which agrees with the Poisson Virasoro algebra of E.Frenkel and N.Reshetikhin and its generalizations and prove its uniqueness (in a natural class of quadratic Poisson structures). The associated hierarchies of nonlinear q-difference equations are also constructed.

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A. L. Pirozerski, M. A. Semenov-Tian-Shansky. 1998-11-05. Generalized q-deformed Gelfand-Dickey structures on the group of q-pseudodifference operators. https://arxiv.org/abs/math/9811025

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