Semisimple Hopf actions on commutative domains
Author(s)Etingof, Pavel I; Walton, Chelsea
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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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Advances in Mathematics
Etingof, Pavel, and Chelsea Walton. “Semisimple Hopf Actions on Commutative Domains.” Advances in Mathematics 251 (January 2014): 47–61.