Quantum groups in higher genus and Drinfeld's new realizations method   ($sl_{2}$ case)
  We define double (central and cocentral) extensions of Manin pairs introduced by Drinfeld, attached to curves and meromorphic differentials. We define ``infinite twistings'' of these pairs and quantize them in the $sl_{2}$ case, adapting Drinfeld's ``new realizations'' technique. We study finite dimensional representations of these algebras in level $0$, and some elliptic examples. 
B. Enriquez and V. Rubtsov