Deformation of algebroid bracket of differential forms and Poisson manifold

2018/06/21 by Alina Dobrogowska, Dobrogowska, Alina, Grzegorz Jakimowicz +3
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1806.08142

openalex publication_date 2018/06/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct the family of algebroid brackets [⋅,⋅]_c,v on the tangent bundle T^*M to a Poisson manifold (M,π) starting from an algebroid bracket of differential forms. We use these brackets to generate Poisson structures on the tangent bundle TM. Next, in the case when M is equipped with a bi-Hamiltonian structure (M,π₁, π₂) we show how to construct another family of Poisson structures. Moreover we present how to find Casimir functions for those structures and we discuss some particular examples.

Related

• Poisson structures on tangent bundles
• On Poisson structures arising from a Lie group action
• The Courant type algebroids, the coadjoint orbits and related integrable flows
• Lifting a Weak Poisson Bracket to the Algebra of Forms
• Deformations of symplectic Lie algebroids, deformations of holomorphic symplectic structures, and index theorems