Poisson Hopf module Fundamental theorem for Hopf group coalgebras

TL;DR

This paper generalizes the fundamental theorem of Poisson Hopf modules to the setting of Hopf group coalgebras, expanding the theoretical framework of Poisson algebra structures in quantum algebra.

Contribution

It extends the fundamental theorem of Poisson Hopf modules from classical Hopf algebras to Hopf group coalgebras, broadening the scope of Poisson module theory.

Findings

Generalization of the fundamental theorem to Hopf group coalgebras

Establishment of conditions for bijective antipode

Framework for Poisson structures in Hopf group coalgebras

Abstract

Let $H$ be a Hopf group coalgebra with a bijective antipode and $A$ an $H$-comodule Poisson algebra. In this paper, we mainly generalize the fundamental theorem of Poisson Hopf modules to the case of Hopf group coalgebras.