A supergeometric approach to Poisson reduction

Abstract

This work introduces a unified approach to the reduction of Poisson manifolds using their description by graded symplectic manifolds. This yields a generalization of the classical Poisson reduction by distributions (Marsden-Ratiu reduction). Further it allows one to construct actions of strict Lie 2-groups and to describe the corresponding reductions.

40 pages. Final version accepted for publication

References in corpus (7)

• Higher-Dimensional Algebra V: 2-Groups
• $Q$-manifolds and Higher Analogs of Lie Algebroids
• Group Objects and Internal Categories
• Mackenzie theory and Q-manifolds
• Higher Lie algebra actions on Lie algebroids
• Graded geometry and Poisson reduction
• An extension of the Marsden-Ratiu reduction for Poisson manifolds

Cited by in corpus (11)

• On homotopy Poisson actions and reduction of symplectic Q-manifolds
• Higher Lie algebra actions on Lie algebroids
• Graded geometry and Poisson reduction
• Reduction of pre-Hamiltonian actions
• Symplectic reduction and a Darboux-Moser-Weinstein theorem for Lie algebroids
• Cosymplectic geometry, reductions, and energy-momentum methods with applications
• Quotients of multiplicative forms and Poisson reduction
• Distributions and quotients on degree 1 NQ-manifolds and Lie algebroids
• The Quaternions and Bott Periodicity Are Quantum Hamiltonian Reductions
• Strong homotopy Lie algebras, homotopy Poisson manifolds and Courant algebroids
• Commutative $n$-ary superalgebras with an invariant skew-symmetric form