On Dynamical Poisson Groupoids I is popular PDF and ePub book, written by Serge Parmentier in 2005-01-27, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, On Dynamical Poisson Groupoids I can be Read Online from any device for your convenience.
On Dynamical Poisson Groupoids I Book PDF Summary
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.
Detail Book of On Dynamical Poisson Groupoids I PDF
- Author : Serge Parmentier
- Release : 27 January 2005
- Publisher : American Mathematical Soc.
- ISBN : 0821865463
- Genre : Mathematics
- Total Page : 92 pages
- Language : English
- PDF File Size : 16,8 Mb
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