## Abstract

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 language | English (US) |
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Pages (from-to) | 25-39 |

Number of pages | 15 |

Journal | Advances in Mathematics |

Volume | 302 |

DOIs | |

State | Published - Oct 22 2016 |

## Keywords

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

## ASJC Scopus subject areas

- Mathematics(all)