Quantization of Lie bialgebras, part VI: quantization of generalized Kac-Moody algebras
| dc.creator | Etingof, Pavel | |
| dc.creator | Kazhdan, David | |
| dc.date | 2000-04-07 | |
| dc.date | 2008-05-15 | |
| dc.date.accessioned | 2026-07-07T09:38:53Z | |
| dc.date.available | 2026-07-07T09:38:53Z | |
| dc.description | This paper is a continuation of the series of papers "Quantization of Lie bialgebras (QLB) I-V". We show that the image of a Kac-Moody Lie bialgebra with the standard quasitriangular structure under the quantization functor defined in QLB-I,II is isomorphic to the Drinfeld-Jimbo quantization of this Lie bialgebra, with the standard quasitriangular structure. This implies that when the quantization parameter is formal, then the category O for the quantized Kac-Moody algebra is equivalent, as a braided tensor category, to the category O over the corresponding classical Kac-Moody algebra, with the tensor category structure defined by a Drinfeld associator. This equivalence is a generalization of the functor constructed previously by G.Lusztig and the second author. In particular, we answer positively a question of Drinfeld whether the characters of irreducible highest weight modules for quantized Kac-Moody algebras are the same as in the classical case. Moreover, our results are valid for the Lie algebra g(A) corresponding to any symmetrizable matrix A (not necessarily with integer entries), which answers another question of Drinfeld. We also prove the Drinfeld-Kohno theorem for the algebra g(A) (it was previously proved by Varchenko using integral formulas for solutions of the KZ equations). | |
| dc.description | 10 pages, amstex; the paper relies on the fact that quantization of Lie bialgebras commutes with duals and doubles, whose proof in the original version contained a gap. An adequate proof of this fact was obtained by Enriquez and Geer in 0707.2337. The present version takes this into account | |
| dc.identifier | https://arxiv.org/abs/math/0004042 | |
| dc.identifier | http://arxiv.org/abs/math/0004042 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/160975 | |
| dc.subject | Quantum Algebra | |
| dc.title | Quantization of Lie bialgebras, part VI: quantization of generalized Kac-Moody algebras | |
| dc.type | text |