On the Gelfand-Kirillov conjecture for quantum algebras

Caldero, Philippe

doi:10.1090/S0002-9939-99-05045-5

On the Gelfand-Kirillov conjecture for quantum algebras
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Proc. Amer. Math. Soc. 128 (2000), 943-951 Request permission

Abstract:

Let $q$ be a complex not a root of unity and $\mathfrak {g}$ be a semi-simple Lie $\mathbb {C}$-algebra. Let $U_{q}(\mathfrak {g})$ be the quantized enveloping algebra of Drinfeld and Jimbo, $U_{q}(\mathfrak {n}^-)\otimes U^{0}\otimes U_{q}(\mathfrak {n})$ be its triangular decomposition, and $\mathbb {C}_{q}[G]$ the associated quantum group. We describe explicitly $\operatorname {Fract} U_{q}(\mathfrak {n})$ and $\operatorname {Fract}\mathbb {C}_{q}[G]$ as a quantum Weyl field. We use for this a quantum analogue of the Taylor lemma.

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