Pointed Hopf actions on fields, II

Pavel Etingof, Chelsea Walton

Research output: Contribution to journalArticlepeer-review


This is a continuation of the authors' study of finite-dimensional pointed Hopf algebras H which act inner faithfully on commutative domains. As mentioned in Part I of this work, the study boils down to the case where H acts inner faithfully on a field. These Hopf algebras are referred to as Galois-theoretical. In this work, we provide classification results for finite-dimensional pointed Galois-theoretical Hopf algebras H of finite Cartan type. Namely, we determine when such H of type A1×r and some H of rank two possess the Galois-theoretical property. Moreover, we provide necessary and sufficient conditions for Reshetikhin twists of small quantum groups to be Galois-theoretical.

Original languageEnglish (US)
Pages (from-to)253-283
Number of pages31
JournalJournal of Algebra
StatePublished - Aug 15 2016


  • Field
  • Finite Cartan type
  • Galois-theoretical
  • Hopf algebra action
  • Pointed

ASJC Scopus subject areas

  • Algebra and Number Theory


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