On the Andreadakis Problem for Subgroups of $IA_n$ - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue International Mathematics Research Notices Année : 2019

## On the Andreadakis Problem for Subgroups of $IA_n$

Jacques Darné
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#### Résumé

Let Fn be the free group on n generators. Consider the group IAn of automorphisms of Fn acting trivially on its abelianization. There are two canonical filtrations on IAn⁠: the 1st one is its lower central series Γ∗⁠; the 2nd one is the Andreadakis filtration A∗⁠, defined from the action on Fn⁠. 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.

#### Domaines

Mathématiques [math]

### Dates et versions

hal-02471026 , version 1 (07-02-2020)

### Identifiants

• HAL Id : hal-02471026 , version 1
• DOI :

### Citer

Jacques Darné. On the Andreadakis Problem for Subgroups of $IA_n$. International Mathematics Research Notices, 2019, rnz237, ⟨10.1093/imrn/rnz237⟩. ⟨hal-02471026⟩

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