On the stable Andreadakis problem

Jacques Darné (1, 2)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 IF - Institut Fourier

Let be the free group on n generators. Consider the group of automorphisms of acting trivially on its abelianization. There are two canonical filtrations on : the first one is its lower central series ⁎; the second one is the Andreadakis filtration ⁎, defined from the action on . In this paper, we establish that the canonical morphism between the associated graded Lie rings ⁎ and ⁎ is stably surjective. We then investigate a p-restricted version of the Andreadakis problem. A calculation of the Lie algebra of the classical congruence group is also included.

Mots clés: Automorphisms of free groups; Filtrations on groups; Lie algebras; Johnson morphisms; Free differential calculus; Congruence groups

Domaines: Mathématiques [math]

Jacques Darné. On the stable Andreadakis problem. Journal of Pure and Applied Algebra, 2019, 223 (12), pp.5484-5525. ⟨10.1016/j.jpaa.2019.04.010⟩. ⟨hal-02468983⟩