%0 Journal Article
%T Universal Drinfeld-Sokolov Reduction and Matrices of Complex Size
%A Boris Khesin
%A Feodor Malikov
%J Physics
%D 1994
%I arXiv
%R 10.1007/BF02101626
%X We construct affinization of the algebra $gl_{\lambda}$ of ``complex size'' matrices, that contains the algebras $\hat{gl_n}$ for integral values of the parameter. The Drinfeld--Sokolov Hamiltonian reduction of the algebra $\hat{gl_{\lambda}}$ results in the quadratic Gelfand--Dickey structure on the Poisson--Lie group of all pseudodifferential operators of fractional order. This construction is extended to the simultaneous deformation of orthogonal and simplectic algebras that produces self-adjoint operators, and it has a counterpart for the Toda lattices with fractional number of particles.
%U http://arxiv.org/abs/hep-th/9405116v2