Incidence Left Loops Derived from Kinematic Algebras

Abstract.

Starting from a suitable kinematic and left alternative ${\mathbb{K}}$-algebra we obtain a class of incidence left loops ${(\mathcal{P}, \mathcal{L}, \cdot)}$ such that every line of ${\mathcal{L}}$ passing through the identity of ${(\mathcal{P}, \cdot)}$ is a commutative subgroup. We investigate the case in which ${(\mathcal{P}, \cdot)}$ is a Moufang loop and we study a class of automorphisms of such a structure.