1999/10/06 by J. Balog, L. Feher, L. Palla · 1 citation
Physics and Astronomy · Mathematics · #hep-th #math-ph #math.MP #math.QA
paper · pdf · doi:10.1016/s0550-3213(99)00738-5
published as Nucl.Phys. B568 (2000) 503-542 · 40 pages, LaTeX
arxiv created 1999/10/06 · arxiv updated 2009/11/30
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.