Selecta Mathematica

, Volume 2, Issue 1, pp 1–41

Quantization of Lie bialgebras, I

  • Pavel Etingof
  • David Kazhdan

DOI: 10.1007/BF01587938

Cite this article as:
Etingof, P. & Kazhdan, D. Selecta Mathematica, New Series (1996) 2: 1. doi:10.1007/BF01587938


In the paper [Dr3] V. Drinfeld formulated a number of problems in quantum group theory. In particular, he raised the question about the existence of a quantization for Lie bialgebras, which arose from the problem of quantization of Poisson Lie groups. When the paper [KL] appeared Drinfeld asked whether the methods of [KL] could be useful for the problem of quantization of Lie bialgebras. This paper gives a positive answer to a number of Drinfeld's questions, using the methods and ideas of [KL]. In particular, we show the existence of a quantization for Lie bialgebras. The universality and functoriality properties of this quantization will be discussed in the second paper of this series. We plan to provide positive answers to most of the remaining questions in [Dr3] in the following papers of this series.

Copyright information

© Birkhäuser Verlag 1996

Authors and Affiliations

  • Pavel Etingof
    • 1
  • David Kazhdan
    • 2
  1. 1.Department of MathematicsHarvard UniversityCambridgeUSA
  2. 2.Department of MathematicsHarvard UniversityCambridgeUSA