Given the definition of a Lie group, namely a group that's a smooth manifold, e.g. https://www.math.stonybrook.edu/~kirillov/mat552/liegroups.pdf and the relevance of Einstein (pre-)derivation, e.g. http://arxiv.org/abs/0802.2137 what would be the interest in regarding groups that are not smooth manifolds?

 The geometric significance, and motivation, comes from looking at Lie groups with left-invariant metrics, however the definition is purely algebraic, at the Lie algebra level.  If you look at algebras over R or C, then its algebra of derivations is the Lie algebra of an algebraic group.  As such, it has a Levi decomposition.  This seems to be enough to carry over the ideas of Nikolayevsky...give it a try!