Moufang symmetry X. Generalized Lie and Maurer-Cartan equations of   continuous Moufang transformations
  The differential equations for a continuous birepresentation of a local analytic Moufang loop are established. The commutation relations for the infinitesimal operators of the representation are found. These commutation relations can be seen as a (minimal) generalization of the Maurer-Cartan equations and do not depend on the particular birepresentation. 
Eugen Paal