| Symbol |
Description |
Location |
| \(\lielayer{\mathfrak{g}}{k}\) |
The homogeneous component of degree \(k\) of a stratified Lie algebra \(\mathfrak{g}\) |
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| \(L_{g}\) |
The left translation by a group element \(g\) |
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| \(\abnormalpolynomial{X}{\covector}\) |
The abnormal polynomial determined by the covector \(\covector\in\mathfrak{g}^*\) and vector \(X\in\mathfrak{g}\) |
Definition 2.1 |
| \(\hallset\) |
A Hall set |
Definition 2.6 |
| \(h\) |
A Hall tree |
Definition 2.6 |
| \(w\) |
A Hall word |
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| \(\freelie{r}\) |
The free Lie algebra of rank \(r\) |
Subsection 2.3 |
| \(\polyring{\hallset}\) |
The weighted multivariate polynomial ring of a free Lie algebra with respect to the Hall set \(\hallset\) |
Definition 2.13 |
| \(XP\) |
The derivative of a polynomial \(P\) by a Lie algebra element \(X\) |
Definition 2.15 |
| \(\covector_{w}\) |
The component of a covector \(\covector\) related to a Hall word \(w\) |
Lemma 2.17 |
| \(\freelie{r,s}\) |
The free nilpotent Lie algebra of rank \(r\) and step \(s\) |
Lemma 3.1 |
| \(\freecarnot{r,s}\) |
The free Carnot group of rank \(r\) and step \(s\) |
Lemma 3.1 |
| \(\lowercentralseriesterm{\mathfrak{g}}{m}\) |
The \(m\text{:}\)th term of the lower central series of \(\mathfrak{g}\) |
Remark 3.3 |
| \(\alpha\star\beta\) |
The concatenation of two curves \(\alpha\) and \(\beta\) |
Subsection 4.2 |