Multiplicative Dirac structures on Lie groups
arXiv:0906.2373 · doi:10.1016/j.crma.2008.10.003
Abstract
We study multiplicative Dirac structures on Lie groups. We show that the characteristic foliation of a multiplicative Dirac structure is given by the cosets of a normal Lie subgroup and, whenever this subgroup is closed, the leaf space inherits the structure of a Poisson-Lie group. We also describe multiplicative Dirac structures on Lie groups infinitesimally.
Published in Comptes Rendus Mathematique
Cited by in corpus (11)
- Quasi-Hamiltonian groupoids and multiplicative Manin pairs
- LA-Courant algebroids and their applications
- VB-algebroid morphisms and representations up to homotopy
- Foliated groupoids and their infinitesimal data
- Poisson Geometry from a Dirac perspective
- Differential forms with values in VB-groupoids
- Infinitesimal Automorphisms of VB-groupoids and algebroids
- Multiplicative Dirac structures
- Integrability of quotients in Poisson and Dirac geometry
- The leaf space of a multiplicative foliation
- Pseudo-Dirac Structures