%0 Journal Article
%T Generalized q-deformed Gelfand-Dickey structures on the group of q-pseudodifference operators
%A A. L. Pirozerski
%A M. A. Semenov-Tian-Shansky
%J Mathematics
%D 1998
%I arXiv
%X 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.
%U http://arxiv.org/abs/math/9811025v1