Balog, J., Dąbrowski, L. and Fehér, L.
(1990)
*Non-standard Quantum Group in Toda and WZNW Theories.*
(Preprint)

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## Abstract

The basic Poisson brackets in the chira.l sectors of the WZNW theory and its Toda reduction are described in terms of a monodromy dependent r-matrix. In the case of the sl(n) Lie algebras, and only then, this monodromy dependence can be ‘gauged away’. The resulting non-trivial solution of the classical Yang-Baxter equation is the classical limit of the quantum R-matrix of the SL(n) Toda theory found recently by Creminer and Gervais. The deformations of SL(n) and U(sl(n)) defined by this R-matrix are studied in the simplest non-trivial case of n = 3. The multiplicative structure of this deformation of U(sl(3)) can be transformed into that of the standard U_q(sl(3)), but the coproduct is different. Possible generalizations for arbitrary n and applications in conformal field theory and in non-commutative differential geometry are briefly indicated. The Cremmer-Gervais R-matrix is ‘Yang-Baxterized’. The resulting spectral parameter dependent R-matrix may give rise to a new series of integrable models.

Item Type: | Article |
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Divisions: | School of Theoretical Physics > Preprints |

Date Deposited: | 19 Jun 2018 14:15 |

Last Modified: | 14 Dec 2022 13:50 |

URI: | https://dair.dias.ie/id/eprint/770 |

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