Inclusion of Loops into Lie Groups: Infinitesimal Characteristics

Abstract

The infinitesimal characteristics for some class of smooth loops generalizing Bruck loops to be embedded into a Lie group are given. The interest to the problem of inclusion of loops into Lie groups has been shown by various recent publications dedicated to representations of loops as transversals on homogeneous spaces. There is presented an example of a smooth left Bol loop, satisfying the generalized Bruck identity, realized as a section on some reductive homogeneous space.