Abstract
We derive a generalization of the classical dynamical Yang–Baxter equation (CDYBE) on a self-dual Lie algebra G by replacing the cotangent bundle T*G in a geometric interpretation of this equation by its Poisson–Lie (PL) analogue associated with a factorizable constant r-matrix on G. The resulting PL-CDYBE, with variables in the Lie group G equipped with the Semenov-Tian-Shansky Poisson bracket based on the constant r-matrix, coincides with an equation that appeared in an earlier study of PL symmetries in the WZNW model. In addition to its new group theoretic interpretation, we present a self-contained analysis of those solutions of the PL-CDYBE that were found in the WZNW context and characterize them by means of a uniqueness result under a certain analyticity assumption.
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Fehér, L., Marshall, I. On a Poisson–Lie Analogue of the Classical Dynamical Yang–Baxter Equation for Self-dual Lie Algebras. Letters in Mathematical Physics 62, 51–62 (2002). https://doi.org/10.1023/A:1021681826447
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DOI: https://doi.org/10.1023/A:1021681826447