2002/08/31 by L. Feher, I. Marshall
Mathematics · Physics and Astronomy · #math.QA #hep-th #math.SG #msc:37J15 #msc:53D17 #msc:17Bxx #msc:81T40
published as Lett.Math.Phys. 62 (2002) 51-62 · 13 pages, LaTeX2e. Typos are corrected in v2, a note added in proof upon publication in LMP is included in v3
arxiv created 2002/12/17 · arxiv updated 2009/11/30
We derive a generalization of the classical dynamical Yang-Baxter equation (CDYBE) on a self-dual Lie algebra \cal 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 \cal 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.