Fundamental theorem of Poisson \((A,H)\)-Hopf modules (Q2068172)

Let \(H\) be a Hopf algebra and \(A\) be a right \(H\)-comodule algebra. Let us recall that a \((A,H)\)-Hopf module is a right \(A\)-module and a right \(H\)-comodule such that the \(A\)-action and the \(H\)-coaction are compatible. The algebra \(A\) could be for example a rational \(G\)-module Poisson algebra where \(G\) is an affine algebraic group. In this paper, the author first recalls the relevant facts about the category of Poisson \((A,H)\)-Hopf modules. Then, he generalizes the fundamental theorem of \((A,H)\)-Hopf modules to Poisson \((A,H)\)-Hopf modules. The relative projectivity in the category of Poisson \((A,H)\)-Hopf modules is also obtained.