On finite-dimensional copointed Hopf algebras over dihedral groups

We classify all finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero such that its coradical is isomorphic to the algebra of functions k<sup>D<sub>m</sub></sup> over a dihedral group D<sub>m</sub>, with m = 4a ≥ 12. We obtain...

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Autores principales: Fantino, Fernando Amado, García, Gastón Andrés, Mastnak, Mitja
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 2019
Materias:
Matemática
Ciencias Exactas
Deformations
Dihedral group
Hopf algebras
Nichols algebras
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/97732
https://ri.conicet.gov.ar/11336/83342
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-97732
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
Ciencias Exactas
Deformations
Dihedral group
Hopf algebras
Nichols algebras
spellingShingle Matemática
Ciencias Exactas
Deformations
Dihedral group
Hopf algebras
Nichols algebras
Fantino, Fernando Amado
García, Gastón Andrés
Mastnak, Mitja
On finite-dimensional copointed Hopf algebras over dihedral groups
topic_facet Matemática
Ciencias Exactas
Deformations
Dihedral group
Hopf algebras
Nichols algebras
description We classify all finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero such that its coradical is isomorphic to the algebra of functions k<sup>D<sub>m</sub></sup> over a dihedral group D<sub>m</sub>, with m = 4a ≥ 12. We obtain this classification by means of the lifting method, where we use cohomology theory to determine all possible deformations. Our result provides an infinite family of new examples of finite-dimensional copointed Hopf algebras over dihedral groups.
format Articulo
Preprint
author Fantino, Fernando Amado
García, Gastón Andrés
Mastnak, Mitja
author_facet Fantino, Fernando Amado
García, Gastón Andrés
Mastnak, Mitja
author_sort Fantino, Fernando Amado
title On finite-dimensional copointed Hopf algebras over dihedral groups
title_short On finite-dimensional copointed Hopf algebras over dihedral groups
title_full On finite-dimensional copointed Hopf algebras over dihedral groups
title_fullStr On finite-dimensional copointed Hopf algebras over dihedral groups
title_full_unstemmed On finite-dimensional copointed Hopf algebras over dihedral groups
title_sort on finite-dimensional copointed hopf algebras over dihedral groups
publishDate 2019
url http://sedici.unlp.edu.ar/handle/10915/97732
https://ri.conicet.gov.ar/11336/83342
work_keys_str_mv AT fantinofernandoamado onfinitedimensionalcopointedhopfalgebrasoverdihedralgroups
AT garciagastonandres onfinitedimensionalcopointedhopfalgebrasoverdihedralgroups
AT mastnakmitja onfinitedimensionalcopointedhopfalgebrasoverdihedralgroups
bdutipo_str Repositorios
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