Journal of Symplectic Geometry
Volume 13 (2015)
Equivalence of the categories of modules over Lie algebroids
Pages: 387 – 419
We study the theory of geometric Morita equivalence in Poisson geometry. A new equivalence relation for integrable Lie algebroids is introduced and investigated. It is shown that two equivalent Lie algebroids have equivalent categories of infinitesimal actions of Lie algebroids. As an application, it is also shown that the Hamiltonian categories for gauge equivalent Dirac structures are equivalent as categories.