Smooth Moufang Loops and Mal’Cev Algebras

Abstract

Here we are going to present the infinitesimal theory of smooth local Moufang loops. Our treatment is based on the infinitesimal theory of smooth local Bol loops elaborated above and the fact that a Moufang loop is nothing more than a left and right Bol loop simultaneously (equivalently, it is a right Bol loop with the left inverse property x−1 . (x.y) = y or with the anti-automorphic inverse property (x. y)−1 = y−1 . x−1). See [V.D. Belousov 67].