An infinitesimal theory of reductive loops (Q1595556)

A smooth loop is called reductive if it is left-monoalternative and a left A-loop simultaneously. On a smooth reductive loop \(Q\) the fundamental right vector fields are constructed. These fields form a triple Lie algebra and define a system of differential equations defining the loop \(Q\). If the fundamental right vector fields of a smooth monoalternative loop \(Q\) form a triple Lie algebra, then this loop is reductive.