Our purpose is to introduce by means of co-adjoint 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 co-adjoint representation on the isotropy Lie algebroid of a Lie groupoid are Lie groupoid. We will call this type of Lie groupoid, co-adjoint Lie groupoid. Also, we try to construct and define Hamiltonian systems on the co-adjoint 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 Hamilton-Jacobi theorem of the Hamiltonian system corresponding to the co-adjoint Lie algebroid.
1
Dept. of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran
Ghorbanali Haghighatdoost; Rezvaneh Ayoubi. Hamiltonian Systems on Co-Adjoint Lie Groupoids. Journal of Lie Theory, Tome 31 (2021) no. 2, pp. 493-516. http://geodesic.mathdoc.fr/item/JOLT_2021_31_2_a10/
@article{JOLT_2021_31_2_a10,
author = {Ghorbanali Haghighatdoost and Rezvaneh Ayoubi},
title = {Hamiltonian {Systems} on {Co-Adjoint} {Lie} {Groupoids}},
journal = {Journal of Lie Theory},
pages = {493--516},
year = {2021},
volume = {31},
number = {2},
url = {http://geodesic.mathdoc.fr/item/JOLT_2021_31_2_a10/}
}
TY - JOUR
AU - Ghorbanali Haghighatdoost
AU - Rezvaneh Ayoubi
TI - Hamiltonian Systems on Co-Adjoint Lie Groupoids
JO - Journal of Lie Theory
PY - 2021
SP - 493
EP - 516
VL - 31
IS - 2
UR - http://geodesic.mathdoc.fr/item/JOLT_2021_31_2_a10/
ID - JOLT_2021_31_2_a10
ER -
%0 Journal Article
%A Ghorbanali Haghighatdoost
%A Rezvaneh Ayoubi
%T Hamiltonian Systems on Co-Adjoint Lie Groupoids
%J Journal of Lie Theory
%D 2021
%P 493-516
%V 31
%N 2
%U http://geodesic.mathdoc.fr/item/JOLT_2021_31_2_a10/
%F JOLT_2021_31_2_a10
