  We study actions of semisimple Hopf algebras H on Weyl algebras A over a
field of characteristic zero. We show that the action of H on A must factor
through a group algebra; in other words, if H acts inner faithfully on A, then
H is cocommutative. The techniques used include reduction modulo a prime number
and the study of semisimple cosemisimple Hopf actions on division algebras.
