Semisimple Hopf actions on commutative domains

Pavel Etingof, Chelsea Walton

Research output: Contribution to journalArticlepeer-review

Abstract

Let H be a semisimple (so, finite dimensional) Hopf algebra over an algebraically closed field k of characteristic zero and let A be a commutative domain over k. We show that if A arises as an H-module algebra via an inner faithful H-action, then H must be a group algebra. This answers a question of E. Kirkman and J. Kuzmanovich and partially answers a question of M. Cohen.The main results of this article extend to working over k of positive characteristic. On the other hand, we obtain results on Hopf actions on Weyl algebras as a consequence of the main theorem.

Original languageEnglish (US)
Pages (from-to)47-61
Number of pages15
JournalAdvances in Mathematics
Volume251
DOIs
StatePublished - Jan 30 2014
Externally publishedYes

Keywords

  • Coideal subalgebra
  • Commutative domain
  • Hopf algebra action
  • Inner faithful
  • Semisimple
  • Weyl algebra

ASJC Scopus subject areas

  • Mathematics(all)

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