Équation de Yang-Baxter dynamique classique et algébroïdes de Lie

Abstract

We interpret the dynamical r-matrices, solutions of the classical dynamical YangBaxter equation, in terms of Lie bialgebroids. Integrating such Lie bialgebroids, we obtain the dynamical Poisson groupoids of Etingof and Varchenko. We thus extend the correspondence between classical r-matrices, coboundary Lie bialgebras and coboundary Poisson-Lie groups to the dynamical case.