ar X iv : h ep - t h / 99 10 04 6 v 1 6 O ct 1 99 9 Chiral Extensions of the WZNW Phase Space , Poisson - Lie Symmetries and Groupoids
نویسندگان
چکیده
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.
منابع مشابه
ar X iv : h ep - t h / 98 08 09 6 v 1 1 7 A ug 1 99 8 Wakimoto realizations of current and exchange algebras ∗
Working at the level of Poisson brackets, we describe the extension of the generalized Wakimoto realization of a simple Lie algebra valued current, J, to a corresponding realization of a group valued chiral primary field, b, that has diagonal monodromy and satisfies Kb ′ = Jb. The chiral WZNW field b is subject to a monodromy dependent exchange algebra, whose derivation is reviewed, too.
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