  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.
