Quantization of Lie bialgebras, part VI: quantization of generalized Kac-Moody algebras

Details Quantization of Lie bialgebras, part VI: quantization of generalized Kac-Moody algebras Quantization of Lie bialgebras, part VI: quantization of generalized Kac-Moody algebras

2000-04-07

arxiv.org/abs/math/0004042v3

Mathematics

Quantum Algebra

10 pages, amstex; the paper relies on the fact that quantization of Lie bialgebras commutes with duals and doubles, whose proo

Scientific paper

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).

Affiliated with

Also associated with

No associations

Rating

Quantization of Lie bialgebras, part VI: quantization of generalized Kac-Moody algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Quantization of Lie bialgebras, part VI: quantization of generalized Kac-Moody algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantization of Lie bialgebras, part VI: quantization of generalized Kac-Moody algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-586209