
Journal of Lie Theory 31 (2021), No. 2, 493516 Copyright Heldermann Verlag 2021 Hamiltonian Systems on CoAdjoint Lie Groupoids Ghorbanali Haghighatdoost Dept. of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran gorbanali@azaruniv.ac.ir Rezvaneh Ayoubi Dept. of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran rezvaneh.ayoubi@azaruniv.ac.ir Our purpose is to introduce by means of coadjoint representation of a Lie groupoid on its isotropy Lie algebroid a class of Lie groupoids. In other words, we show that the orbits of the coadjoint representation on the isotropy Lie algebroid of a Lie groupoid are Lie groupoid. We will call this type of Lie groupoid, coadjoint Lie groupoid. Also, we try to construct and define Hamiltonian systems on the coadjoint Lie groupoids. By considering the trivial Lie groupoid as an example, we show that our construction can be considered as a generalization of the construction of the Lie groups to the Lie groupoids. Finally we present the types I and II of HamiltonJacobi theorem of the Hamiltonian system corresponding to the coadjoint Lie algebroid. Keywords: Lie groupoids, Lie algebroids, Hamiltonian system, HamiltonJacobi equation. MSC: 18B40, 53D17, 70H08, 70H20. [ Fulltextpdf (180 KB)] for subscribers only. 