Continuous Moufang transformations (Q1383851)

By analogy to Lie groups, the representation theory of smooth Moufang loops is developed. Since the right and the left actions of a Moufang loop on a set are different (non-equivalent) the so-called birepresentations are used. For them the generalized Lie equations and the structure equations of the corresponding infinitesimal operators are found. The equations (7), (9) from the paper under review are the same thing as the relations (37) from a paper by \textit{M. A. Akivis} and \textit{A. M. Shelekhov} [in Webs and quasigroups, Tver, 20-32 (1993; Zbl 0792.53009)].