Poisson structure on predual of Banach Lie algebroid

TL;DR

This paper constructs a linear Poisson structure on the predual of a Banach Lie algebroid, offering an alternative approach to known results and exploring the existence of queer Banach Lie algebroids with an example.

Contribution

It introduces a new method for constructing the Poisson structure on the predual of Banach Lie algebroids and discusses queer Banach Lie algebroids.

Findings

Established a linear Poisson structure on the predual bundle.

Presented an example of a precotangent bundle.

Discussed the existence of queer Banach Lie algebroids.

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.