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Bi-Galois objects over the Taft algebras

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Abstract

Letk be a field. We study the groupoid of Hopf bi-Galois objects, whose objects arek-Hopf algebras, and whose morphisms areL-H-bi-Galois extensions ofk for Hopf algebrasL andH.

We show that ifH=H N,m is one of the Taft algebras, thenL≅HN,m in anyL-H-bi-Galois object. We compute the group of bi-Galois objects over the two-generator Taft algebrasH N,1. We classify the isomorphism classes of Galois extensions ofk over the general Taft algebrasH N,m, and we compute the groups of bi-Galois objects overH N,m for oddN.

Our computations for the two-generator Taft algebras rely on Masuoka's classification [9] of their cleft extensions. To treat the general Taft algebras, we will generalize a result of Kreimer [6] to give a description of the Galois objects over a tensor product of two Hopf algebras.

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  1. Mathematisches Institut der Universität München, Theresienstr. 39, 80333, München, Germany

    Peter Schauenburg

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  1. Peter Schauenburg
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Schauenburg, P. Bi-Galois objects over the Taft algebras. Isr. J. Math. 115, 101–123 (2000). https://doi.org/10.1007/BF02810582

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  • DOI: https://doi.org/10.1007/BF02810582

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