Rigidity of Graded Regular Algebras

Authors :: Kirkman, E.
Kuzmanovich, J.
Zhang, J. J.
Publication Year :: 2007
Abstract: 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.<br />Comment: 39 pages To be published in Transactions of the American Mathematical Society