Induction and coinduction for Hopf algebras: Applications
type: Item
instance of: scholarly article
title: Induction and coinduction for Hopf algebras: Applications
zbMATH Open document ID: 0808.16042
published in: Journal of Algebra
publication date: 1995-01-12T00:00:00Z
full work available at URL: https://hdl.handle.net/10067/999040151162165141
review text: Let \(H\) be a finite dimensional and semisimple Hopf algebra, and \(A\) an \(H\)-module algebra. The authors study the induced and coinduced functors from the ring of invariants of \(A\) and show, in analogy with Theorem 1.1 of \textit{C. Năstăsescu} [J. Algebra 120, 119-138 (1989; Zbl 0678.16001)] that they arise in adjoint pairs. This result is subsequently applied to Clifford theory, and also to give a description of injective envelopes in the category of modules over the smash product \(A\# H\). In the last part a similar result is obtained for induction and coinduction from semi-invariants.
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 16S40
Mathematics Subject Classification ID: 16D90
Mathematics Subject Classification ID: 16W50
Mathematics Subject Classification ID: 16E30
Mathematics Subject Classification ID: 16D50
zbMATH DE Number: 589936
zbMATH Keywords: semisimple Hopf algebra
zbMATH Keywords: \(H\)-module algebra
zbMATH Keywords: induced and coinduced functors
zbMATH Keywords: ring of invariants
zbMATH Keywords: Clifford theory
zbMATH Keywords: injective envelopes
zbMATH Keywords: category of modules
zbMATH Keywords: smash product
zbMATH Keywords: semi-invariants
author: Stefaan Caenepeel
author: Serban Raianu
author: Fred Van Oystaeyen
reviewed by: José L. Gómez-Pardo
MaRDI profile type: Publication
OpenAlex ID: W2067558172
DOI: 10.1006/JABR.1994.1107
description: scientific article; zbMATH DE number 589936