Poisson structure on predual of Banach Lie algebroid

2025/05/19 by Tomasz Goliński, Goliński, Tomasz, Grzegorz Jakimowicz +1 · 1 citation
Mathematics · Medicine · #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Homotopy and Cohomology in Algebraic Topology #Intracerebral and Subarachnoid Hemorrhage Research #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.2505.13351

openalex publication_date 2025/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct the linear Poisson structure on the predual bundle of a Banach Lie algebroid. It is an alternative approach to the already known results on the linear sub-Poisson structure on the dual bundle. We also discuss the existence of queer Banach Lie algebroids. An example of a precotangent bundle is presented.

Citations

• Poisson structures in the Banach setting: comparison of different approaches
• Weak Poisson structures on infinite dimensional manifolds and hamiltonian actions
• Banach Lie algebroids
• Differential calculus on a Lie algebroid and Poisson manifolds
• Linear almost Poisson structures and Hamilton-Jacobi equation. Applications to nonholonomic Mechanics
• The restricted Grassmannian, Banach Lie-Poisson spaces, and coadjoint orbits
• Symplectic leaves in real Banach Lie-Poisson spaces

Cited by

• A note on precotangent bundles: the example of Grassmannians

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