2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64751We 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.13 pages, LaTeX2e. Typos are corrected in v2, a note added in proof upon publication in LMP is included in v3Quantum AlgebraHigh Energy Physics - TheorySymplectic Geometry37J15, 53D17, 17Bxx, 81T40text