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.
Original language | English (US) |
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Pages (from-to) | 47-61 |
Number of pages | 15 |
Journal | Advances in Mathematics |
Volume | 251 |
DOIs | |
State | Published - Jan 30 2014 |
Externally published | Yes |
Keywords
- Coideal subalgebra
- Commutative domain
- Hopf algebra action
- Inner faithful
- Semisimple
- Weyl algebra
ASJC Scopus subject areas
- General Mathematics