Some isomorphism results for graded twistings of function algebras on finite groups

Bichon, Julien; Paradis, Maeva

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 31 (2022) no. 2, pp. 501-544.

Nous obtenons des résultats de classification à isomorphisme près pour les algèbres de Hopf obtenues comme twists gradués d’algèbres de fonctions sur des groupes finis par des actions cocentrales de groupes cycliques Plus généralement, nous considérons le problème d’isomor-phisme pour les algèbres de Hopf de dimension finie s’insérant dans des extensions cocentrales abéliennes. Nous appliquons ensuite nos résultats de classification à divers exemples concrets impliquant les groupes spéciaux linéaires sur des corps finis, les groupes symétriques et alternés, et les groupes diédraux.

We provide isomorphism results for Hopf algebras that are obtained as graded twistings of function algebras on finite groups by cocentral actions of cyclic groups. More generally, we also consider the isomorphism problem for finite-dimensional Hopf algebras fitting into abelian cocentral extensions. We apply our classification results to a number of concrete examples involving special linear groups over finite fields, alternating and symmetric groups, and dihedral groups.

Classification : 16T05
Keywords: Finite-dimensional Hopf algebras, graded twist, abelian cocentral extension
Mots clés : Algèbres de Hopf de dimension finie, twist gradué, extension cocentrale abélienne

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