Gauge deformations for Hopf algebras with the dual Chevalley property.
type: Item
instance of: scholarly article
zbMATH Open document ID: 1257.16023
DOI: 10.1142/S0219498811005798
author: Alessandro Ardizzoni
author: Margaret Beattie
author: Claudia Menini
publication date: 2012-06-25T00:00:00Z
full work available at URL: https://arxiv.org/abs/1012.4935
Mathematics Subject Classification ID: 16T05
Mathematics Subject Classification ID: 16T10
Mathematics Subject Classification ID: 16S40
zbMATH DE Number: 6049617
zbMATH Keywords: Hopf algebras
zbMATH Keywords: dual Chevalley property
zbMATH Keywords: cocycle twists
zbMATH Keywords: dual quasi-Hopf algebras
zbMATH Keywords: gauge transformations
zbMATH Keywords: quasi-bialgebras
zbMATH Keywords: Yetter-Drinfel'd modules
MaRDI profile type: Publication
arXiv ID: 1012.4935
cites work: Triangular Hopf algebras with the Chevalley property
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cites work: Small bialgebras with a projection.
cites work: Lazy cohomology: an analogue of the Schur multiplier for arbitrary Hopf algebras.
cites work: Radford's biproduct for quasi-Hopf algebras and bosonization
cites work: Braided bialgebras and quadratic blalgebras
cites work: Characters of Hopf algebras
cites work: The structure of Hopf algebras with a weak projection
cites work: The wedderburn-malcev theorem for comodule algebras
OpenAlex ID: W2963594644
published in: Journal of Algebra and its Applications
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title: Gauge deformations for Hopf algebras with the dual Chevalley property.
review text: Let \(A\) be a Hopf algebra over a field \(K\) of characteristic zero such that its coradical \(H\) is a finite-dimensional sub-Hopf algebra. Then, the Hopf algebra \(A\) has the dual Chevalley property. In this paper, the authors mainly show that there is a gauge transformation \(\zeta\) on \(A\) such that \(A^\zeta\cong Q\#H\), where \(A^\zeta\) is the dual quasi-bialgebra obtained from \(A\) by twisting its multiplication by \(\zeta\), \(Q\) is a connected dual quasi-bialgebra in \(^H_H\mathcal {YD}\) (the category of left Yetter-Drinfel'd modules) and \(Q\#H\) is a dual quasi-bialgebra called the bosonization of \(Q\) by \(H\).
reviewed by: Liangyun Zhang
description: scientific article; zbMATH DE number 6049617