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Fundamental theorem of Poisson Hopf modules for braided Hopf algebras | Synapse

January 26, 2026

Fundamental theorem of Poisson Hopf modules for braided Hopf algebras

Key Points

The central aim is to establish a theorem related to K-Poisson (A,H)-Hopf modules in the context of braided Hopf algebras.
Proved injectivity of K-Poisson (A,H)-Hopf module M under specific conditions.
Analyzed the properties of a K-Poisson algebra A as an H-comodule.
Explored the implications of quasi-commutativity in Hopf algebra H.
Confirmed that an injective K-Poisson A-module implies injectivity as a K-Poisson (A,H)-Hopf module.
Established a fundamental theorem regarding K-Poisson (A,H)-Hopf modules.

Abstract

Let (K,R) be a triangular Hopf algebra with the universal R-matrix R. Let H be a braided Hopf algebra associated with (K,R) and A a K-Poisson algebra. Assume that A is an H-comodule Poisson algebra. In this paper, we will firstly prove that for a K-Poisson (A,H)-Hopf module M, when H is quasi-commutative and M is an injective K-Poisson A-module, M is an injective K-Poisson (A,H)-Hopf module. Then we will give the fundamental theorem of K-Poisson (A,H)-Hopf modules.

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Cite This Study

Lu et al. (Fri,) studied this question.

synapsesocial.com/papers/69770370722626c4468e87a1 https://doi.org/https://doi.org/10.1142/s0219498827501453