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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the Gelfand-Kirillov conjecture
for quantum algebras


Author: Philippe Caldero
Journal: Proc. Amer. Math. Soc. 128 (2000), 943-951
MSC (1991): Primary 17Bxx
Published electronically: July 28, 1999
MathSciNet review: 1625709
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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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Additional Information

Philippe Caldero
Affiliation: Institut Girard Desargues, UPRS-A-5028, Université Claude Bernard Lyon I, Bat 101, 69622 Villeurbanne Cedex, France
Email: caldero@desargues.univ-lyon1.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05045-5
PII: S 0002-9939(99)05045-5
Keywords: Quantum groups, quantum Weyl fields, R-matrix
Received by editor(s): March 27, 1997
Received by editor(s) in revised form: May 15, 1998
Published electronically: July 28, 1999
Communicated by: Roe Goodman
Article copyright: © Copyright 2000 American Mathematical Society