ISBN-10:
0821836730
ISBN-13:
9780821836736
Pub. Date:
01/27/2005
Publisher:
American Mathematical Society
On Dynamical Poisson Groupoids I (Memoirs of the American Mathematical Society Series, No. 824)

On Dynamical Poisson Groupoids I (Memoirs of the American Mathematical Society Series, No. 824)

by Luen-Chau Li, Serge Parmentier

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Overview

On Dynamical Poisson Groupoids I (Memoirs of the American Mathematical Society Series, No. 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.

Product Details

ISBN-13: 9780821836736
Publisher: American Mathematical Society
Publication date: 01/27/2005
Series: Memoirs of the American Mathematical Society Series , #824
Pages: 72
Product dimensions: 6.92(w) x 9.96(h) x 0.23(d)

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