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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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.
References
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Additional Information
  • E. Kirkman
  • Affiliation: Department of Mathematics, Wake Forest University, P.O. Box 7388, Winston-Salem, North Carolina 27109
  • MR Author ID: 101920
  • 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
  • MR Author ID: 314509
  • Email: zhang@math.washington.edu
  • Received by editor(s): November 6, 2006
  • Published electronically: June 26, 2008
  • © Copyright 2008 American Mathematical Society
  • 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
  • MathSciNet review: 2434290