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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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A class of counterexamples to the Gel’fand-Kirillov conjecture
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by Jacques Alev, Alfons Ooms and Michel Van den Bergh PDF
Trans. Amer. Math. Soc. 348 (1996), 1709-1716 Request permission

Abstract:

Let $G$ be a connected non-special semisimple algebraic group and let $W$ be a finite dimensional $G$-representation such that $W$ has trivial generic stabilizer. Let $\mathfrak {g}=\text {Lie}(G)$. Then the semi-direct product $\mathfrak {g}\oplus W$ is a counter-example to the Gel′fand-Kirillov conjecture.
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Additional Information
  • Jacques Alev
  • Affiliation: Université de Reims, UFR des Sciences, Département de Mathématiques, Moulin de la Housse, BP 347, 51062 Reims Cedex
  • MR Author ID: 24605
  • Email: jle@ccr.jussieu.fr, jacques.alev@cleo.univ-reims.fr
  • Alfons Ooms
  • Affiliation: Limburgs Universitair Centrum, Departement WNI, Universitaire Campus, 3590 Diepenbeek, Belgium
  • Email: aooms@luc.ac.be
  • Michel Van den Bergh
  • MR Author ID: 176980
  • Email: vdbergh@luc.ac.b
  • Received by editor(s): February 22, 1995
  • Additional Notes: The third author is a senior researcher at the NFWO
  • © Copyright 1996 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 348 (1996), 1709-1716
  • MSC (1991): Primary 17B35; Secondary 16K40
  • DOI: https://doi.org/10.1090/S0002-9947-96-01465-1
  • MathSciNet review: 1321564