Bracket width of simple Lie algebras - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Documenta Mathematica Année : 2021

Bracket width of simple Lie algebras

Boris Kunyavskii
  • Fonction : Auteur
Andriy Regeta
  • Fonction : Auteur

Résumé

The notion of commutator width of a group, defined as the smallest number of commutators needed to represent each element of the derived group as their product, has been extensively studied over the past decades. In particular, in 1992 Barge and Ghys discovered the first example of a simple group of commutator width greater than one among groups of diffeomorphisms of smooth manifolds. We consider a parallel notion of bracket width of a Lie algebra and present the first examples of simple Lie algebras of bracket width greater than one. They are found among the algebras of polynomial vector fields on smooth affine varieties.

Dates et versions

hal-03379157 , version 1 (14-10-2021)

Identifiants

Citer

Adrien Dubouloz, Boris Kunyavskii, Andriy Regeta. Bracket width of simple Lie algebras. Documenta Mathematica , 2021, 26, pp.1601-1627. ⟨10.25537/dm.2021v26.1601-1627⟩. ⟨hal-03379157⟩
32 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More