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.
- Exchange algebra
- Poisson-Lie symmetry
- WZNW model
ASJC Scopus subject areas
- Nuclear and High Energy Physics