### Abstract

The chiral WZNW symplectic form Ω^{ρ}_{chir} is inverted in the general case. Thereby a precise relationship between the arbitrary monodromy dependent 2-form appearing in Ω^{ρ}_{chir} and the exchange r-matrix that governs the Poisson brackets of the group valued chiral fields is established. The exchange r-matrices are shown to satisfy a new dynamical generalization of the classical modified Yang-Baxter (YB) equation and Poisson-Lie (PL) groupoids are constructed that encode this equation analogously as PL groups encode the classical YB equation. For an arbitrary simple Lie group G, exchange r-matrices are found that are in one-to-one correspondence with the possible PL structures on G and admit them as PL symmetries.

Original language | English |
---|---|

Pages (from-to) | 503-542 |

Number of pages | 40 |

Journal | Nuclear Physics B |

Volume | 568 |

Issue number | 3 |

Publication status | Published - Mar 6 2000 |

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### Keywords

- Exchange algebra
- Poisson-Lie symmetry
- WZNW model

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

**Chiral extensions of the WZNW phase space, Poisson-Lie symmetries and groupoids.** / Balog, J.; Fehér, L.; Palla, L.

Research output: Contribution to journal › Article

*Nuclear Physics B*, vol. 568, no. 3, pp. 503-542.

}

TY - JOUR

T1 - Chiral extensions of the WZNW phase space, Poisson-Lie symmetries and groupoids

AU - Balog, J.

AU - Fehér, L.

AU - Palla, L.

PY - 2000/3/6

Y1 - 2000/3/6

N2 - The chiral WZNW symplectic form Ωρchir is inverted in the general case. Thereby a precise relationship between the arbitrary monodromy dependent 2-form appearing in Ωρchir and the exchange r-matrix that governs the Poisson brackets of the group valued chiral fields is established. The exchange r-matrices are shown to satisfy a new dynamical generalization of the classical modified Yang-Baxter (YB) equation and Poisson-Lie (PL) groupoids are constructed that encode this equation analogously as PL groups encode the classical YB equation. For an arbitrary simple Lie group G, exchange r-matrices are found that are in one-to-one correspondence with the possible PL structures on G and admit them as PL symmetries.

AB - The chiral WZNW symplectic form Ωρchir is inverted in the general case. Thereby a precise relationship between the arbitrary monodromy dependent 2-form appearing in Ωρchir and the exchange r-matrix that governs the Poisson brackets of the group valued chiral fields is established. The exchange r-matrices are shown to satisfy a new dynamical generalization of the classical modified Yang-Baxter (YB) equation and Poisson-Lie (PL) groupoids are constructed that encode this equation analogously as PL groups encode the classical YB equation. For an arbitrary simple Lie group G, exchange r-matrices are found that are in one-to-one correspondence with the possible PL structures on G and admit them as PL symmetries.

KW - Exchange algebra

KW - Poisson-Lie symmetry

KW - WZNW model

UR - http://www.scopus.com/inward/record.url?scp=0034610870&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034610870&partnerID=8YFLogxK

M3 - Article

VL - 568

SP - 503

EP - 542

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 3

ER -