Quantization of Lie bialgebras, I

Details Quantization of Lie bialgebras, I Quantization of Lie bialgebras, I

1995-06-06

arxiv.org/abs/q-alg/9506005v4

Mathematics

Quantum Algebra

40 pages, amstex. The new version contains several changes throughout the paper suggested by the referee of Selecta Math. In p

Scientific paper

In the paper "On some unsolved problems in quantum group theory", V.Drinfeld formulated the problem of the existence of a universal quantization for Lie bialgebras. When the paper "Tensor structures arising from affine Lie algebras, III", by Kazhdan and Lusztig, appeared, Drinfeld asked whether its methods could be useful for the problem of universal quantization of Lie bialgebras. In this paper we use these methods to construct the universal quantization, which gives a positive answer to Drinfeld's question. We also show the existence of universal quantization of classical r-matrices, unitary r-matrices, and quasitriangular Lie bialgebras, which answers the corresponding questions of Drinfeld.

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