Finite dimensional Hopf actions on Weyl algebras

Juan Cuadra, Pavel Etingof, Chelsea Walton

Research output: Contribution to journalArticlepeer-review


We prove that any action of a finite dimensional Hopf algebra H on a Weyl algebra A over an algebraically closed field of characteristic zero factors through a group action. In other words, Weyl algebras do not admit genuine finite quantum symmetries. This improves a previous result by the authors, where the statement was established for semisimple H. The proof relies on a refinement of the method previously used: namely, considering reductions of the action of H on A modulo prime powers rather than primes. We also show that the result holds, more generally, for algebras of differential operators. This gives an affirmative answer to a question posed by the last two authors.

Original languageEnglish (US)
Pages (from-to)25-39
Number of pages15
JournalAdvances in Mathematics
StatePublished - Oct 22 2016


  • Algebra of differential operators
  • Hopf algebra action
  • Reduction modulo prime powers
  • Weyl algebra

ASJC Scopus subject areas

  • Mathematics(all)


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