Mathematics – Quantum Algebra
Scientific paper
1998-11-05
Mathematics
Quantum Algebra
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.
Pirozerski A. L.
Semenov-Tian-Shansky M. A.
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