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

Mathematics – Quantum Algebra

Scientific paper

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34 pages, AMSLATEX

Scientific paper

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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