Finitely generated invariants of Hopf algebras on free associative   algebras
  We show that the invariants of a free associative algebra of finite rank under a linear action of a finite-dimensional Hopf algebra generated by group-like and skew-primitive elements form a finitely generated algebra exactly when the action is scalar. This generalizes an analogous result for group actions by automorphisms obtained by Dicks and Formanek, and Kharchenko. 
Vitor O. Ferreira, Lucia S. I. Murakami