Irreducible actions and faithful actions of hopf algebras

Jeffrey Bergen, Miriam Cohen, Davida Fischman

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


Let H be a Hopf algebra acting on an algebra A. We will examine the relationship between A, the ring of invariants A H, and the smash product A # H. We begin by studying the situation where A is an irreducible A # H module and, as an application of our first main theorem, show that if D is a division ring then [D : D H]≦dim H. 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 of A # H is strongly related to the faithfulness of the left and right actions of A # H on A.

Original languageEnglish
Pages (from-to)5-18
Number of pages14
JournalIsrael Journal of Mathematics
Issue number1-2
StatePublished - 1 Feb 1990

ASJC Scopus subject areas

  • General Mathematics


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