Inductions and coinductions for Hopf extensions
type: Item
instance of: scholarly article
title: Inductions and coinductions for Hopf extensions
zbMATH Open document ID: 0878.16021
author: Xu Yonghua
author: Yinhuo Zhang
author: Fred Van Oystaeyen
published in: Science in China. Series A
publication date: 1997-11-10T00:00:00Z
review text: When \(H\) is a finite dimensional Hopf algebra, the concept of \(H\)-Galois extensions for \(H\)-comodule algebras has a dual in terms of \(H\)-modules \(A\); this involves the surjectivity of the Morita maps for \(A\), \(A\#H\) and \(A^{\text{co}H}\). The authors study induction and coinduction functors for both types of extensions. The paper gives (for example) a functorial characterization of Hopf extensions with elements of trace 1: such an element exists if and only if the induced and coinduced functors from the Hopf module category to the invariant module category are isomorphic. They also prove that some of the good properties of Hopf Galois extensions are in fact separability conditions on suitable functors.
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 16D90
Mathematics Subject Classification ID: 18A40
Mathematics Subject Classification ID: 18A22
zbMATH DE Number: 908302
zbMATH Keywords: separability conditions on functors
zbMATH Keywords: finite dimensional Hopf algebras
zbMATH Keywords: \(H\)-Galois extensions
zbMATH Keywords: \(H\)-comodule algebras
zbMATH Keywords: Morita maps
zbMATH Keywords: induction and coinduction functors
zbMATH Keywords: functorial characterization of Hopf extensions
zbMATH Keywords: Hopf module categories
zbMATH Keywords: Hopf Galois extensions
reviewed by: Davida Fischman
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 908302