  We study the existence of various types of gradings on Lie algebras, such as
Carnot gradings or gradings in positive integers, and prove that the existence
of such gradings is invariant under extensions of scalars.
  As an application, we prove that if G is a finitely generated nilpotent
group, its systolic growth is asymptotically equivalent to its word growth if
and only if the Malcev completion of G is Carnot.
  We also characterize when G is non-cohopfian, in terms of the existence of a
non-trivial grading in non-negative integers, and deduce that this property
only depends on its real (or even complex) Malcev completion.
