Formal symplectic groupoid

Details Formal symplectic groupoid Formal symplectic groupoid

2003-12-19

arxiv.org/abs/math/0312380v1

Comm. Math. Phys. 253 (2005), no. 3, 645--674.

Mathematics

Symplectic Geometry

28 pages, 4 figures

Scientific paper

The multiplicative structure of the trivial symplectic groupoid over $\mathbb R^d$ associated to the zero Poisson structure can be expressed in terms of a generating function. We address the problem of deforming such a generating function in the direction of a non-trivial Poisson structure so that the multiplication remains associative. We prove that such a deformation is unique under some reasonable conditions and we give the explicit formula for it. This formula turns out to be the semi-classical approximation of Kontsevich's deformation formula. For the case of a linear Poisson structure, the deformed generating function reduces exactly to the CBH formula of the associated Lie algebra. The methods used to prove existence are interesting in their own right as they come from an at first sight unrelated domain of mathematics: the Runge--Kutta theory of the numeric integration of ODE's.

Affiliated with

Also associated with

No associations

Rating

Formal symplectic groupoid does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Formal symplectic groupoid, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Formal symplectic groupoid will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-198876