Manin triples for double Lie bialgebroids
arXiv:2505.16605 · doi:10.1016/j.geomphys.2025.105710
Abstract
We verify that LA-Courant algebroids provide the Manin triple framework for double Lie bialgebroids. Specifically, we establish a correspondence between double Lie bialgebroids and LA-Manin triples, i.e., LA-Courant algebroids equipped with a pair of complementary LA-Dirac structures. As an application, LA-Courant algebroids and CA-groupoids given by Drinfeld doubles are shown to correspond via integration and differentiation.
19 pages