Hopf extensions of algebras and Maschke type theorems
type: Item
instance of: scholarly article
title: Hopf extensions of algebras and Maschke type theorems
zbMATH Open document ID: 0731.16025
DOI: 10.1007/BF02764613
author: Yukio Doi
published in: Israel Journal of Mathematics
publication date: 1990-01-01T00:00:00Z
review text: Let A be a Hopf algebra. An A-extension B/C is an A-comodule algebra B with invariant subalgebra C. An (A,B)-Hopf module is an A-comodule and a B-module such that the comodule structure map is a B-module homomorphism. The paper gives sufficient conditions (1) that B/C is an A-Galois extension, (2) that A-Galois extensions are separable, (3) that exact sequences of B-modules which split as C-modules also split as B-modules, (4) that exact sequences of (A,B)-Hopf modules which split as B-modules also split as (A,B)-Hopf modules, (5) that B is semisimple artinian and (6) that B is a C-Frobenius extension.
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 16D70
Mathematics Subject Classification ID: 16W20
zbMATH DE Number: 4208319
zbMATH Keywords: Hopf algebra
zbMATH Keywords: comodule algebra
zbMATH Keywords: A-Galois extensions
zbMATH Keywords: exact sequences
zbMATH Keywords: Hopf modules
zbMATH Keywords: Frobenius extension
reviewed by: Bodo Pareigis
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4208319