A Family of Left Lie Bol Loops

Abstract

In this paper the left Bol split extension method is used to build left Bol Lie loops from the Lie groups H and K such that H is a Lie subgroup of Aut(K). Furthermore, we investigated some of the properties of those loops constructed in this way. Examples are given for finite and infinite dimensional left Bol Lie loops. Moreover, we showed that the twisted semidirect product of Lie algebras is an Akivis algebra.