Israel Journal of Mathematics

, Volume 72, Issue 1–2, pp 5–18 | Cite as

Irreducible actions and faithful actions of hopf algebras

  • Jeffrey Bergen
  • Miriam Cohen
  • Davida Fischman


LetH be a Hopf algebra acting on an algebraA. We will examine the relationship betweenA, the ring of invariantsA H, and the smash productA # H. We begin by studying the situation whereA is an irreducibleA # H module and, as an application of our first main theorem, show that ifD is a division ring then [D : D H]≦dimH. We next show that prime rings with central rings of invariants satisfy a polynomial identity under the action of certain Hopf algebras. Finally, we show that the primeness ofA # H is strongly related to the faithfulness of the left and right actions ofA # H onA.


Hopf Algebra Left Ideal Prime Ring Division Ring Polynomial Identity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© The Weizmann Science Press of Israel 1990

Authors and Affiliations

  • Jeffrey Bergen
    • 1
  • Miriam Cohen
    • 2
  • Davida Fischman
    • 3
  1. 1.DePaul UniversityChicagoUSA
  2. 2.Ben Gurion University of the NegevBeer ShevaIsrael
  3. 3.Weizmann Institute of ScienceRehovotIsrael

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