On finite-dimensional copointed Hopf algebras over dihedral groups
type: Item
instance of: scholarly article
title: On finite-dimensional copointed Hopf algebras over dihedral groups
zbMATH Open document ID: 1456.16031
author: Fernando Fantino
author: Gastón Andrés García
author: Mitja Mastnak
published in: Journal of Pure and Applied Algebra
publication date: 2019-04-25T00:00:00Z
full work available at URL: https://arxiv.org/abs/1608.06167
full work available at URL: http://hdl.handle.net/11336/83342
review text: Let \(k\) be an algebraically closed field of characteristic zero, and denote by \(\mathbb{D}_m\) the dihedral group of order \(2m\) for any \(m\geq 3\). The aim of the paper is to classify the finite dimensional Hopf algebras with coradical \((k\mathbb{D}_m)^*\), the dual of the group Hopf algebra of \(\mathbb{D}_m\), for \(m=4a\geq 12\). The approach uses the lifting method, which is very efficient for classifying Hopf algebras with coradical a Hopf subalgebra, deformation theory and some cohomological methods for classifying the liftings.
reviewed by: Sorin Dascalescu
Mathematics Subject Classification ID: 16T05
zbMATH DE Number: 7047913
zbMATH Keywords: Nichols algebras
zbMATH Keywords: Hopf algebras
zbMATH Keywords: dihedral group
zbMATH Keywords: deformations
Wikidata QID: Q105627890
MaRDI profile type: Publication
OpenAlex ID: W2963647262
arXiv ID: 1608.06167
cites work: Lifting via cocycle deformation.
cites work: Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type. III: Semisimple classes in \(\mathrm{PSL}_n(q)\)
cites work: Q5503565
cites work: Finite-dimensional pointed Hopf algebras with alternating groups are trivial.
cites work: Pointed Hopf algebras over the sporadic simple groups.
cites work: Q4944224
cites work: Q3153375
cites work: Finite Dimensional Hopf Algebras Over the Dual Group Algebra of the Symmetric Group in Three Letters
cites work: Liftings of Nichols algebras of diagonal type II: All liftings are cocycle deformations
cites work: On rigidity of Nichols algebras
cites work: Poincaré-Birkhoff-Witt theorem for quadratic algebras of Koszul type
cites work: Quantum lines over non-cocommutative cosemisimple Hopf algebras.
cites work: Braided bialgebras and quadratic blalgebras
cites work: On Graded Bialgebra Deformations
cites work: On pointed Hopf algebras over dihedral groups.
cites work: Deformation by cocycles of pointed Hopf algebras over non-abelian groups.
cites work: Finite-dimensional pointed or copointed Hopf algebras over affine racks.
cites work: Copointed Hopf algebras over \(\mathbb{S}_4\)
cites work: Bialgebra cohomology, deformations, and quantum groups.
cites work: Rank 2 Nichols algebras with finite arithmetic root system
cites work: Bialgebra cohomology, pointed Hopf algebras, and deformations.
cites work: Bialgebras of type one*
cites work: Hopf Algebras
cites work: Q5590089
DOI: 10.1016/J.JPAA.2018.11.021
description: scientific article