### Abstract

We derive a generalization of the classical dynamical Yang-Baxter equation (CDYBE) on a self-dual Lie algebra G by replacing the cotangent bundle T*G in a geometric interpretation of this equation by its Poisson-Lie (PL) analogue associated with a factorizable constant r-matrix on G. The resulting PL-CDYBE, with variables in the Lie group G equipped with the Semenov-Tian-Shansky Poisson bracket based on the constant r-matrix, coincides with an equation that appeared in an earlier study of PL symmetries in the WZNW model. In addition to its new group theoretic interpretation, we present a self-contained analysis of those solutions of the PL-CDYBE that were found in the WZNW context and characterize them by means of a uniqueness result under a certain analyticity assumption.

Original language | English |
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Pages (from-to) | 51-62 |

Number of pages | 12 |

Journal | Letters in Mathematical Physics |

Volume | 62 |

Issue number | 1 |

DOIs | |

Publication status | Published - Oct 1 2002 |

### Keywords

- Classical dynamical Yang-Baxter equation
- Poisson-Lie groups and groupoids
- Self-dual Lie algebra, Wess-Zumino-Novikov-Witten model

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics