Rigidity of graded regular algebras

Kirkman, E.; Kuzmanovich, J.; Zhang, J.

doi:10.1090/S0002-9947-08-04571-6

Rigidity of graded regular algebras
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by E. Kirkman, J. Kuzmanovich and J. J. Zhang PDF

Trans. Amer. Math. Soc. 360 (2008), 6331-6369 Request permission

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.

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