  We prove a graded version of Alev-Polo's rigidity theorem: the homogenization
of the universal enveloping algebra of a semisimple Lie algebra and the Rees
ring of the Weyl algebras $A_n(k)$ cannot be isomorphic to their fixed subring
under any finite group action. We also show the same result for other classes
of graded regular algebras including the Sklyanin algebras.
