Reduction of Poisson manifolds with Hamiltonian Lie algebroids

2024/11/17 by Hirota, Yuji, Ikeda, Noriaki
#53D20 (Primary) 53D17 #70G45 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2411.10969

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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