# Drinfeld–Sokolov Reduction for Difference Operators and Deformations of -Algebras¶I. The Case of Virasoro Algebra

@article{Frenkel1998DrinfeldSokolovRF, title={Drinfeld–Sokolov Reduction for Difference Operators and Deformations of -Algebras¶I. The Case of Virasoro Algebra }, author={Edward Frenkel and Nikolai Reshetikhin and Michael Arsen'evich Semenov-Tian-Shansky}, journal={Communications in Mathematical Physics}, year={1998}, volume={192}, pages={605-629} }

Abstract:We propose a q-difference version of the Drinfeld-Sokolov reduction scheme, which gives us q-deformations of the classical -algebras by reduction from Poisson-Lie loop groups. We consider in detail the case of SL2. The nontrivial consistency conditions fix the choice of the classical r-matrix defining the Poisson-Lie structure on the loop group LSL2, and this leads to a new elliptic classical r-matrix. The reduced Poisson algebra coincides with the deformation of the classical Virasoro…

## 40 Citations

### Drinfeld–Sokolov Reduction for Difference Operators and Deformations of W-Algebras¶ II. The General Semisimple Case

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Abstract:The paper is the sequel to [9]. We extend the Drinfeld--Sokolov reduction procedure to q-difference operators associated with arbitrary semisimple Lie algebras. This leads to a new elliptic…

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Abstract: We construct a discrete quantum version of the Drinfeld–Sokolov correspondence for the sine-Gordon system. The classical version of this correspondence is a birational Poisson morphism…

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Abstract:The paper is the sequel to [9]. We extend the Drinfeld--Sokolov reduction procedure to q-difference operators associated with arbitrary semisimple Lie algebras. This leads to a new elliptic…

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