Mathematics > Symplectic Geometry
[Submitted on 17 Nov 2024]
Title:Reduction of Poisson manifolds with Hamiltonian Lie algebroids
View PDF HTML (experimental)Abstract:Reduction theorem for Poisson manifolds with Hamiltonian Lie algebroids is presented. The notion of compatibility of a momentum section is introduced to the category of Hamiltonian Lie algebroids over Poisson manifolds. It is shown that a compatible momentum section is a Lie algebra homomorphism, and then the quotient space of the zero level set of a compatible momentum section proves to be a Poisson manifold.
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