Fundamental theorem of Poisson \((A,H)\)-Hopf modules
type: Item
instance of: scholarly article
title: Fundamental theorem of Poisson \((A,H)\)-Hopf modules
zbMATH Open document ID: 1484.17035
author: T. Guédénon
published in: Journal of Algebra
publication date: 2022-01-19T00:00:00Z
review text: 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.
reviewed by: Angela Gammella-Mathieu
Mathematics Subject Classification ID: 17B63
Mathematics Subject Classification ID: 16T05
zbMATH DE Number: 7459403
zbMATH Keywords: Poisson algebra
zbMATH Keywords: Poisson module
zbMATH Keywords: Hopf algebra
zbMATH Keywords: comodule Poisson algebra
zbMATH Keywords: Poisson Hopf module
zbMATH Keywords: (A,H)-Hopf modules
zbMATH Keywords: A-action
zbMATH Keywords: H-coaction
Wikidata QID: Q115193871
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2021.12.017
OpenAlex ID: W4200580554
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DOI: 10.1016/J.JALGEBRA.2021.12.017
description: scientific article; zbMATH DE number 7459403