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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A class of counterexamples to
the Gel´fand-Kirillov conjecture


Authors: Jacques Alev, Alfons Ooms and Michel Van den Bergh
Journal: Trans. Amer. Math. Soc. 348 (1996), 1709-1716
MSC (1991): Primary 17B35; Secondary 16K40
MathSciNet review: 1321564
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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
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
Email: vdbergh@luc.ac.b

DOI: http://dx.doi.org/10.1090/S0002-9947-96-01465-1
PII: S 0002-9947(96)01465-1
Keywords: Gel-fand-Kirillov conjecture
Received by editor(s): February 22, 1995
Additional Notes: The third author is a senior researcher at the NFWO
Article copyright: © Copyright 1996 American Mathematical Society