  Let $F\_n$ be the free group on $n$ generators. Consider the group $IA\_n$ of
automorphisms of $F\_n$ acting trivially on its abelianization. There are two
canonical filtrations on $IA\_n$: the first one is its lower central series
$\Gamma\_*$; the second one is the Andreadakis filtration $\mathcal A\_*$,
defined from the action on $F\_n$. The Andreadakis problem consists in
understanding the difference between these filtrations. Here, we show that they
coincide when restricted to the subgroup of triangular automorphisms, and to
the pure braid group.
