A note on a paper by Cuadra, Etingof and Walton

ABSTRACT

We analyze the proof of the main result of a paper by Cuadra, Etingof and Walton, which says that any action of a semisimple Hopf algebra H on the nth Weyl algebra A = A_n(K) over a field K of characteristic 0 factors through a group algebra. We verify that their methods can be used to show that any action of a semisimple Hopf algebra H on an iterated Ore extension of derivation type $A=K[x_1;d_1][x_2;d_2][\cdots ][x_n;d_n]$ in characteristic zero factors through a group algebra.

KEYWORDS:

• Inner faithful action
• iterated Ore extensions
• semisimple Hopf algebras

1991 MATHEMATICS SUBJECT CLASSIFICATION:

• 13A35
• 16T05

Acknowledgments

We would like to thank Chelsea Walton and Pavel Etingof very much for many clarifications about their papers [4, 3]. In particular we would like to thank Chelsea Walton for her careful reading of our manuscript and her constructive comments. Thanks go also to the very detailed and constructive comments of the referee. Further thanks go to Ken Brown, Paula Carvalho, Jörg Feldvoss, André Leroy and Jurek Matczuk for helpful discussions.