dorsal/arxiv
View SchemaDrinfeld-Sokolov reduction for difference operators and deformations of W-algebras I. The case of Virasoro algebra
| Authors | E. Frenkel, N. Reshetikhin, M. A. Semenov-Tian-Shansky |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9704011 |
| URL | https://arxiv.org/abs/q-alg/9704011 |
| DOI | 10.1007/s002200050311 |
Abstract
We propose a q-difference version of the Drinfeld-Sokolov reduction scheme, which gives us q-deformations of the classical W-algebras by reduction from Poisson-Lie loop groups. We consider in detail the case of SL(2). The nontrivial consistency conditions fix the choice of the classical r-matrix defining the Poisson-Lie structure on the loop group LSL(2), 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 q-alg/9505025. We also consider a discrete analogue of this Poisson algebra. In the second part (q-alg/9702016) the construction is generalized to the case of an arbitrary semisimple Lie algebra.
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"abstract": "We propose a q-difference version of the Drinfeld-Sokolov reduction scheme,\nwhich gives us q-deformations of the classical W-algebras by reduction from\nPoisson-Lie loop groups. We consider in detail the case of SL(2). The\nnontrivial consistency conditions fix the choice of the classical r-matrix\ndefining the Poisson-Lie structure on the loop group LSL(2), and this leads to\na new elliptic classical r-matrix. The reduced Poisson algebra coincides with\nthe deformation of the classical Virasoro algebra previously defined in\nq-alg/9505025. We also consider a discrete analogue of this Poisson algebra. In\nthe second part (q-alg/9702016) the construction is generalized to the case of\nan arbitrary semisimple Lie algebra.",
"arxiv_id": "q-alg/9704011",
"authors": [
"E. Frenkel",
"N. Reshetikhin",
"M. A. Semenov-Tian-Shansky"
],
"categories": [
"q-alg",
"math.QA"
],
"doi": "10.1007/s002200050311",
"title": "Drinfeld-Sokolov reduction for difference operators and deformations of W-algebras I. The case of Virasoro algebra",
"url": "https://arxiv.org/abs/q-alg/9704011"
},
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