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ISSN 1088-6850(e) ISSN 0002-9947(p)

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

Author(s): Jacques Alev; Alfons Ooms; 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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