Noriaki Ikeda: Hamiltonian Lie algebroids: physical applications and cohomological descriptions

Abstract

A Hamiltonian Lie algebroid generalizes the theory of a momentum map and a Hamiltonian G-space over a symplectic manifold with a Lie group action to the setting of Lie groupoids. This structure was introduced by Blohmann and Weinstein. Similar structures have also been studied by Kotov and Strobl as compatibility conditions for a Lie algebroid with other structures.

Many well-known and significant physical models exhibit this structure. After explaining the definition, I present a simple physical model that possesses a Hamiltonian Lie algebroid structure. I then provide its cohomological description based on the BFV formalism of this physical model.