Annales Mathématiques
Blaise Pascal
no. 2
Examples of polynomial identities distinguishing the Galois objects over finite-dimensional Hopf algebras
[Exemples d’identités polynomiales distinguant les objets galoisiens d’une algèbre de Hopf de dimension finie]
Christian Kassel1
1 Institut de Recherche Mathématique Avancée, CNRS & Université de Strasbourg, 7 rue René Descartes, 67084 Strasbourg, France
Annales mathématiques Blaise Pascal, Tome 20 (2013) no. 2, pp. 175-191.

Nous définissons le concept d’identité polynomiale pour une algèbre-comodule sur une algèbre de Hopf H. Nous présentons des identités polynomiales explicites distinguant à isomorphisme près les objets galoisiens d’une algèbre de Taft ou de l’algèbre de Hopf E(n).

We define polynomial H-identities for comodule algebras over a Hopf algebra H and establish general properties for the corresponding T-ideals. In the case H is a Taft algebra or the Hopf algebra E(n), we exhibit a finite set of polynomial H-identities which distinguish the Galois objects over H up to isomorphism.

DOI : 10.5802/ambp.325
Classification : 16R50, 16T05, 16T15
Keywords: Hopf algebra, comodule algebra, polynomial identity
Mot clés : algèbre de Hopf, algèbre-comodule, identité polynomiale

Christian Kassel 1

1 Institut de Recherche Mathématique Avancée, CNRS & Université de Strasbourg, 7 rue René Descartes, 67084 Strasbourg, France 
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Christian Kassel. Examples of polynomial identities distinguishing the Galois objects over finite-dimensional Hopf algebras. Annales mathématiques Blaise Pascal, Tome 20 (2013) no. 2, pp. 175-191. doi : 10.5802/ambp.325. https://ambp.centre-mersenne.org/articles/10.5802/ambp.325/

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