Israel Journal of Mathematics

, Volume 72, Issue 1, pp 5–18

Irreducible actions and faithful actions of hopf algebras

  • Jeffrey Bergen
  • Miriam Cohen
  • Davida Fischman

DOI: 10.1007/BF02764609

Cite this article as:
Bergen, J., Cohen, M. & Fischman, D. Israel J. Math. (1990) 72: 5. doi:10.1007/BF02764609


LetH be a Hopf algebra acting on an algebraA. We will examine the relationship betweenA, the ring of invariantsAH, 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 : DH]≦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.

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