On the stable Andreadakis problem
Document type :
Compte-rendu et recension critique d'ouvrage
Title :
On the stable Andreadakis problem
Author(s) :
Journal title :
Journal of Pure and Applied Algebra
Pages :
5484-5525
Publisher :
Elsevier
Publication date :
2019-12
ISSN :
0022-4049
English keyword(s) :
Automorphisms of free groups
Filtrations on groups
Lie algebras
Johnson morphisms
Free differential calculus
Congruence groups
Filtrations on groups
Lie algebras
Johnson morphisms
Free differential calculus
Congruence groups
HAL domain(s) :
Mathématiques [math]
English abstract : [en]
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 ...
Show more >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.Show less >
Show more >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.Show less >
Language :
Anglais
Popular science :
Non
ANR Project :
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