Tomasz Goliński
Poisson structures and Banach Lie algebroids
In finite dimension there is an equivalence between Lie algebroids and linear Poisson structures on its dual. In Banach case the situation turns out to be more complicated. Namely the Lie algebroid structure no longer leads to a Poisson bracket defined for all smooth functions on the dual. As demonstrated by F. Pelletier and P. Cabau, one can still define a kind of weak Poisson (or sub-Poisson) bracket on some subalgebra of smooth functions. However as an alternative approach one can replace the dual of the Lie algebroid by the predual and obtain stronger results. An example of a precotangent bundle is presented. The existence of queer Banach Lie algebroids will also be briefly discussed.
