The Use of Hopf Algebras in the Lie Theory of Loops Related to Reductive Homogeneous Spaces

In his generalization of reductive homogeneous spaces, Lev Sabinin introduced hyporeductive and pseudoreductive local loops. Sabinin proved that these loops admit a satisfactory Lie theoretical approach. In this paper we derive Sabinin's results in an algebraic context by means of nonassociative Hopf algebras that encode the information about the nonassociative products of these local loops.