Generic Hopf Galois extensions

  • Christian Kassel


In previous joint work with Eli Aljadeff we attached a generic Hopf Galois extension \( A_H^\alpha \) to each twisted algebra \( {}^\alpha H \) obtained from a Hopf algebra H by twisting its product with the help of a cocycle α. The algebra \( A_H^\alpha \) is a flat deformation of \( {}^\alpha H \) over a “big” central subalgebra \( B_H^\alpha \) and can be viewed as the noncommutative analogue of a versal torsor in the sense of Serre. After surveying the results on \( A_H^\alpha \) obtained with Aljadeff, we establish three new results: we present a systematic method to construct elements of the commutative algebra \( B_H^\alpha \), we show that a certain important integrality condition is satisfied by all finite-dimensional Hopf algebras generated by grouplike and skew-primitive elements, and we compute \( B_H^\alpha \) in the case where H is the Hopf algebra of a cyclic group.


Hopf Algebra Galois Extension Algebra Morphism Grouplike Element Pointed Hopf Algebra 
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© Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden GmbH 2011

Authors and Affiliations

  • Christian Kassel
    • 1
  1. 1.Institut de Recherche Mathématique AvancéeUniversité de Strasbourg CNRSStrasbourgFrance

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