Geodesic
Matched pairs of Lie algebroids
Glasgow mathematical journal, Tome 39 (1997) no. 2, pp. 167-181

Voir la notice de l'article provenant de la source Cambridge University Press

We extend to Lie algebroids the notion variously known as a double Lie algebra (Lu and Weinstein), matched pair of Lie algebras (Majid), or twilled extension of Lie algebras (Kosmann-Schwarzbach and Magri). It is proved that a matched pair of Lie groupoids induces a matched pair of Lie algebroids. Conversely, we show that under certain conditions a matched pair of Lie algebroids integrates to a matched pair of Lie groupoids. The importance of matched pairs of Lie algebroids has been recently demonstrated by Lu. 
Mokri, Tahar. Matched pairs of Lie algebroids. Glasgow mathematical journal, Tome 39 (1997) no. 2, pp. 167-181. doi: 10.1017/S0017089500032055
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