Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4605955 | Differential Geometry and its Applications | 2014 | 24 Pages |
Abstract
Let G be a connected Lie group and g its Lie algebra. We denote by â0 the torsion free bi-invariant linear connection on G given by âX0Y=12[X,Y], for any left invariant vector fields X,Y. A Poisson structure on g is a commutative and associative product on g for which adu is a derivation, for any uâg. A torsion free bi-invariant linear connections on G which have the same curvature as â0 are called special. We show that there is a bijection between the space of special connections on G and the space of Poisson structures on g. We compute the holonomy Lie algebra of a special connection and we show that the Poisson structures associated to special connections which have the same holonomy Lie algebra as â0 possess interesting properties. Finally, we study Poisson structures on a Lie algebra and we give a large class of examples which gives, of course, a large class of special connections.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Saïd Benayadi, Mohamed Boucetta,