Poisson Bracket in Diffeology
Monday, March 27, 2023
In this note we show how to understand the Poisson bracket in diffeology, working directly on the group of Hamiltonian diffeo- morphisms and bypassing tangent spaces. It seems a priori to be a contravariant object and therefore not very suitable for diffeology, but it can be defined in a covariant way, which is more suitable for the diffeology framework.

Ref. http://math.huji.ac.il/~piz/documents/DBlog-Rmk-PBID.pdf