• DOI:10.1007/s002200050311
• Corpus ID: 6489645

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 Vladimir Frenkel and Nikolai Reshetikhin and Michael Arsen'evich Semenov-Tian-Shansky},
  journal={Communications in Mathematical Physics},
  year={1998},
  volume={192},
  pages={605-629}
}

• E. Frenkel, N. Reshetikhin, M. Semenov-Tian-Shansky
• Published 11 April 1997
• Mathematics
• Communications in Mathematical Physics

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 algebra previously defined in [19]. We also consider a discrete analogue of this Poisson algebra. In the second part [31] the construction is generalized to the case of an arbitrary semisimple Lie algebra.