Lie Algebroids Associated to Poisson Actions

Details Lie Algebroids Associated to Poisson Actions Lie Algebroids Associated to Poisson Actions

1995-03-08

arxiv.org/abs/q-alg/9503003v1

Mathematics

Differential Geometry

35 pages

Scientific paper

This work is motivated by a result of Drinfeld on Poisson homogeneous spaces. For each Poisson manifold $P$ with a Poisson action by a Poisson Lie group $G$, we describe a Lie algebroid structure on the direct sum vector bundle $P \times {\frak g} \oplus T^*P$, where ${\frak g}$ is the Lie algebra of $G$. It is built out of the transformation Lie algebroid $P \times {\frak g}$ and the cotangent bundle Lie algebroid $T^*P$ together with a pair of representations of them on each other. When the action of $G$ on $P$ is transitive, the kernel of the anchor map of this Lie algebroid gives a Lie algebra bundle over $P$, the fibers of which are given by Drinfeld. As applications, we describe the symplectic leaves and the $G$-invariant Poisson cohomology of Poisson homogeneous $G$-spaces.

Affiliated with

Also associated with

No associations

Rating

Lie Algebroids Associated to Poisson Actions 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 Lie Algebroids Associated to Poisson Actions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Lie Algebroids Associated to Poisson Actions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-152906