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arXiv · 1301.4161

Semisimple Hopf actions on commutative domains

Pavel Etingof·Chelsea Walton
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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.

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BibTeXRIS

Pavel Etingof, Chelsea Walton. 2013-10-08. Semisimple Hopf actions on commutative domains. https://arxiv.org/abs/1301.4161

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