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Rigidity of graded regular algebras


Authors: E. Kirkman, J. Kuzmanovich and J. J. Zhang
Journal: Trans. Amer. Math. Soc. 360 (2008), 6331-6369
MSC (2000): Primary 16E10, 16W30, 20J05
DOI: https://doi.org/10.1090/S0002-9947-08-04571-6
Published electronically: June 26, 2008
MathSciNet review: 2434290
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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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Additional Information

E. Kirkman
Affiliation: Department of Mathematics, Wake Forest University, P.O. Box 7388, Winston-Salem, North Carolina 27109
Email: kirkman@wfu.edu

J. Kuzmanovich
Affiliation: Department of Mathematics, Wake Forest University, P.O. Box 7388, Winston-Salem, North Carolina 27109
Email: kuz@wfu.edu

J. J. Zhang
Affiliation: Department of Mathematics, University of Washington, Box 354350, Seattle, Washington 98195
Email: zhang@math.washington.edu

DOI: https://doi.org/10.1090/S0002-9947-08-04571-6
Keywords: Artin-Schelter regular algebra, group action, reflection, trace, Hilbert series, fixed subring, quantum polynomial rings
Received by editor(s): November 6, 2006
Published electronically: June 26, 2008
Article copyright: © Copyright 2008 American Mathematical Society

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