Finite dimensional Hopf actions on Weyl algebras
Name
Etingof_Finite dimensional.pdf
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192.35 KB
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Adobe PDF
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Author(s)
Cuadra, Juan
Walton, Chelsea
Etingof, Pavel I
Date Issued
July 2016
Journal
Advances in Mathematics
Publisher
Elsevier BV
Citation
Cuadra, Juan et al. “Finite Dimensional Hopf Actions on Weyl Algebras.” Advances in Mathematics 302 (October 2016): 25–39 © 2016 Elsevier Inc.
Version
Original manuscript
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. Keywords: Hopf algebra action; Weyl algebra; Algebra of differential operators; Reduction modulo prime powers
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-NonCommercial-NoDerivs License
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1016/J.AIM.2016.07.009
