Weakly Hamiltonian actions

Abstract

In this paper we generalize constructions of non-commutative integrable systems to the context of weakly Hamiltonian actions on Poisson manifolds. In particular we prove that abelian weakly Hamiltonian actions on symplectic manifolds split into Hamiltonian and non-Hamiltonian factors, and explore generalizations in the Poisson setting.

10 pages, the paper has been rewritten with a focus on the Poisson setting. Motivating examples have been added. The final version will appear at the Journal of Geometry and Physics

Cited by in corpus (1)

• Non-commutative integrable systems on $b$-symplectic manifolds