I have a nilpotent lie group $N$ with upper central series $$1 = N_0 \triangleleft N_1 \triangleleft \dots \triangleleft N_k = N$$ which induces the filtration $$0 = \mathfrak{n}_0 \subset \mathfrak{n}_1 \subset \dots \subset \mathfrak{n}_k = \mathfrak{n}$$ of the Lie algebra $\mathfrak{n}$.

For convenience, I've defined the *level* of a vector $\xi \in \mathfrak{n}$ to be the smallest $i$ such that $\xi \in \mathfrak{n}_i$. I assume this concept has a standardized name, either in the context of filtrations or in the context of nilpotent Lie algebras. What would this standardized name be?

`$x \in \mathfrak{n}_i \setminus \mathfrak{n}_{i-1}$`

. $\endgroup$ – Jim Humphreys May 25 '10 at 14:56`$d(x) :=i$`

" without making up a word. $\endgroup$ – Jim Humphreys May 25 '10 at 16:41