Manin triples on multiplicative Courant algebroids
arXiv:2505.01276 · doi:10.1016/j.difgeo.2025.102273
Abstract
We extend the characterization of Lie bialgebroids via Manin triples to the context of double structures over Lie groupoids. We consider Lie bialgebroid groupoids, given by LA-groupoids in duality, and establish their correspondence with multiplicative Manin triples, i.e., CA-groupoids equipped with a pair of complementary multiplicative Dirac structures. As an application, we give a new viewpoint to the co-quadratic Lie algebroids of Lang, Qiao, and Yin (2021) and the Manin triple description of Lie bialgebroid crossed modules.
arXiv comment15 pages
References in corpus (9)
- Courant algebroids, derived brackets and even symplectic supermanifolds
- Vector bundles over Lie groupoids and algebroids
- Linear and multiplicative 2-forms
- Q-groupoids and their cohomology
- LA-Courant algebroids and their applications
- Lie 2-bialgebras
- Weak Lie 2-bialgebra
- Hitchhiker's Guide to Courant Algebroid Relations
- Transitive Courant algebroids and double symplectic groupoids