Examples of polynomial identities distinguishing the Galois objects over finite-dimensional Hopf algebras

Kassel, Christian

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 $E\left(n\right)$.

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 $E\left(n\right)$, we exhibit a finite set of polynomial $H$-identities which distinguish the Galois objects over $H$ up to isomorphism.

Classification : 16R50, 16T05, 16T15
Keywords: Hopf algebra, comodule algebra, polynomial identity
Mot clés : algèbre de Hopf, algèbre-comodule, identité polynomiale

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