Nichols algebras of U_q(g)-modules
  A technique is developed to reduce the investigation of Nichols algebras of integrable U_q(g)-modules to the investigation of Nichols algebras of braided vector spaces with diagonal braiding. The results are applied to obtain information on the Gelfan'd-Kirillov dimension of these Nichols algebras and their defining relations if the braiding is of a special type and q is not a root of unity.   For simple g the cases of finite Gelfand-Kirillov dimension are determined completely. 
Stefan Ufer