On Dynamical Poisson Groupoids I - Couverture souple

Li, Luen-Chau; Parmentier, Serge

Couverture souple

ISBN 10 : 0821836730 ISBN 13 : 9780821836736

Editeur : American Mathematical Society, 2005

Synopsis

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.

Détails de l'édition

• Éditeur: American Mathematical Society
• Date d'édition: 2005
• Langue: anglais
• ISBN 10: 0821836730
• ISBN 13: 9780821836736
• Reliure: Broché
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible