Mathematics

Every quiver determines an associative algebra on which one can define geometric objects such as symplectic forms and Poisson brackets. This opens up the possibility of considering abstract Hamiltonian systems on such algebras, inducing (a family of) ordinary Hamiltonian systems on the representation spaces of the corresponding quiver. These systems may be "integrable" in various senses of the word. The goal of this talk is to show some examples of the different situations that may arise.