Galois objects over generalized Drinfeld doubles, with an application to \(u_q({\mathfrak sl}_2)\)
type: Item
instance of: scholarly article
title: Galois objects over generalized Drinfeld doubles, with an application to \(u_q({\mathfrak sl}_2)\)
zbMATH Open document ID: 0956.16018
author: Peter Schauenburg
published in: Journal of Algebra
publication date: 2000-12-13T00:00:00Z
review text: The author obtains some general results about Galois objects over twisted tensor products and over normal quotient Hopf algebras. He applies these ideas to the finite Hopf algebra \(u_q({\mathfrak sl}_2)\) when \(q\) is a root of unity. This is a quotient of the Drinfeld double of a Taft algebra by a normal Hopf subalgebra. His methods thus yield all cleft extensions of \(u_q({\mathfrak sl}_2)\). This is a special case of a result of \textit{R. Günther} in his thesis [Univ. München (1998; Zbl 0956.16016)], who used different methods involving the diamond lemma.
Mathematics Subject Classification ID: 16W30
Mathematics Subject Classification ID: 17B37
zbMATH DE Number: 1340562
zbMATH Keywords: Galois objects
zbMATH Keywords: twisted tensor products
zbMATH Keywords: quotient Hopf algebras
zbMATH Keywords: finite Hopf algebras
zbMATH Keywords: Drinfeld doubles
zbMATH Keywords: Taft algebras
zbMATH Keywords: cleft extensions
reviewed by: Earl J. Taft
MaRDI profile type: Publication
full work available at URL: jabr.1998.7814
OpenAlex ID: W2010782160
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DOI: 10.1006/JABR.1998.7814
description: scientific article; zbMATH DE number 1340562