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

Alev, Jacques; Ooms, Alfons; Van den Bergh, Michel

doi:10.1090/S0002-9947-96-01465-1

A class of counterexamples to the Gel’fand-Kirillov conjecture
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by Jacques Alev, Alfons Ooms and Michel Van den Bergh

Trans. Amer. Math. Soc. 348 (1996), 1709-1716

DOI: https://doi.org/10.1090/S0002-9947-96-01465-1

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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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