  We call a finite, spanning set of a semi-simple real Lie algebra a
distinguished set if it satisfies the following property: The Lie bracket of
any two elements out of the set is, up to some constant, another element in the
set; conversely, for any element in the set, there are two elements out of the
set whose Lie bracket is, up to some constant, the given element. We show in
the paper that every semi-simple real Lie algebra has a distinguished set.
