Quasi-Poisson Manifolds

http://dx.doi.org/10.4153/CJM-2002-001-5
Canad. J. Math. 54(2002), 3-29

  Published:2002-02-01
 Printed: Feb 2002

A quasi-Poisson manifold is a $G$-manifold equipped with an invariant bivector field whose Schouten bracket is the trivector field generated by the invariant element in $\wedge^3 \g$ associated to an invariant inner product. We introduce the concept of the fusion of such manifolds, and we relate the quasi-Poisson manifolds to the previously introduced quasi-Hamiltonian manifolds with group-valued moment maps.