Semisimple Hopf actions on commutative domains
Name
Eingof_Semisimple Hopf.pdf
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220.53 KB
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Adobe PDF
Checksum (MD5)
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Author(s)
Etingof, Pavel I
Walton, Chelsea
Date Issued
October 2013
Journal
Advances in Mathematics
Publisher
Elsevier
Citation
Etingof, Pavel, and Chelsea Walton. “Semisimple Hopf Actions on Commutative Domains.” Advances in Mathematics 251 (January 2014): 47–61.
Version
Original manuscript
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.
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.2013.10.008
