Rigidity of Graded Regular Algebras

2007/06/05 by Ellen Kirkman, Kirkman, E., James Kuzmanovich +3 · 1 citation
Mathematics · #16A62 (Primary) #16E70 #16W30 #20J50 (Secondary) #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.0706.0662

openalex publication_date 2007/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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