  The Hopf actions on vertex operator algebras are investigated. If the action
is semisimple, a Schur-Weyl type decomposition is obtained. When the Hopf
algebra is finite dimensional and the action is faithful, the action is a group
action. Moreover if the Hopf algebra is finite dimensional and the action is
semisimple and inner faithful, the action is also a group action. In this case,
inner faithfulness is equivalent to faithfulness.
