Freeness of Hopf algebras over semisimple group-like subalgebras
type: Item
instance of: scholarly article
title: Freeness of Hopf algebras over semisimple group-like subalgebras
zbMATH Open document ID: 0649.16007
DOI: 10.1016/0021-8693(88)90050-6
author: M. Bettina Zoeller
published in: Journal of Algebra
publication date: 1988-01-01T00:00:00Z
review text: Let H be a finite-dimensional Hopf algebra over a field k, G(H) its group of group-like elements (i.e., elements \(g\neq 0\) in H with \(\Delta g=g\otimes g)\). Let L be a subgroup of G(H). The author proves that if kL is semisimple, i.e., char k does not divide \(| L|\), then H is free as left kL-module. Use is made of criteria developed by \textit{D. E. Radford} [J. Pure Appl. Algebra 11, 15-28 (1977; Zbl 0367.16004)] for Hopf algebras to be free modules over group-like subalgebras. \{Reviewer's note: W. D. Nichols and the author have recently removed the restriction that kL be semisimple. In fact, they have more recently shown that a finite-dimensional Hopf algebra is a free module over any Hopf subalgebra.\}
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 16S10
zbMATH DE Number: 4059605
zbMATH Keywords: finite-dimensional Hopf algebra
zbMATH Keywords: group-like elements
zbMATH Keywords: free modules over group-like subalgebras
reviewed by: Earl J. Taft
MaRDI profile type: Publication
full work available at URL: 0021-8693(88)90050-6
OpenAlex ID: W2039249748
cites work: Q5340151
cites work: Q5250139
cites work: The Order of the Antipode of a Finite Dimensional Hopf Algebra is Finite
cites work: Pointed Hopf algebras are free over Hopf subalgebras
cites work: Freeness (projectivity) criteria for Hopf algebras over Hopf subalgebras
cites work: Q5590089
description: scientific article; zbMATH DE number 4059605