Memoirs of the American Mathematical Society 2005; 72 pp; softcover Volume: 174 ISBN10: 0821836730 ISBN13: 9780821836736 List Price: US$62 Individual Members: US$37.20 Institutional Members: US$49.60 Order Code: MEMO/174/824
 We address the question of duality for the dynamical Poisson groupoids of Etingof and Varchenko over a contractible base. We also give an explicit description for the coboundary case associated with the solutions of (CDYBE) on simple Lie algebras as classified by the same authors. Our approach is based on the study of a class of Poisson structures on trivial Lie groupoids within the category of biequivariant Poisson manifolds. In the former case, it is shown that the dual Poisson groupoid of such a dynamical Poisson groupoid is isomorphic to a Poisson groupoid (with trivial Lie groupoid structure) within this category. In the latter case, we find that the dual Poisson groupoid is also of dynamical type modulo Poisson groupoid isomorphisms. For the coboundary dynamical Poisson groupoids associated with constant \(r\)matrices, we give an explicit construction of the corresponding symplectic double groupoids. In this case, the symplectic leaves of the dynamical Poisson groupoid are shown to be the orbits of a Poisson Lie group action. Table of Contents  Introduction
 A class of biequivariant Poisson groupoids
 Duality
 An explicit case study of duality
 Coboundary dynamical Poisson groupoids  the constant \(r\)matrix case
 Appendix
 Bibliography
