Quantization of Lie bialgebras,I

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.