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

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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.

Original languageEnglish
Pages (from-to)503-542
Number of pages40
JournalNuclear Physics B
Issue number3
Publication statusPublished - Mar 6 2000


  • Exchange algebra
  • Poisson-Lie symmetry
  • WZNW model

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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