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Chiral Extensions of the WZNW Phase Space, Poisson-Lie Symmetries and Groupoids

J. Balog·L. Feher·L. Palla
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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.

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J. Balog, L. Feher, L. Palla. 1999-10-06. Chiral Extensions of the WZNW Phase Space, Poisson-Lie Symmetries and Groupoids. https://doi.org/10.1016/s0550-3213(99)00738-5

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