Finite Representations of the braid group commutator subgroup

Abdelouahab Arouche (1)

1 LATN - Laboratoire d'Algèbre et Théorie des Nombres

We study the representations of the commutator subgroup K_{n} of the braid group B_{n} into a finite group . This is done through a symbolic dynamical system. Some experimental results enable us to compute the number of subgroups of K_{n} of a given (finite) index, and, as a by-product, to recover the well known fact that every representation of K_{n} into S_{r} , with n > r , must be trivial.

Mots clés: groupe des tresses; représentation; dynamique symbolique; groupe symétrique

Domaines: Systèmes dynamiques [math.DS]

Abdelouahab Arouche. Finite Representations of the braid group commutator subgroup. 2007. ⟨hal-00141712⟩