Geodesic
Bracket width of simple Lie algebras
Documenta mathematica, Tome 26 (2021), pp. 1601-1627.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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 [Math. Ann. 294, No. 2, 235--265 (1992; Zbl 0894.55006)] \textit{J. Barge} and \textit{E. Ghys} discovered the first example of a simple group of commutator width greater than one among groups of diffeomorphisms of smooth manifolds. \par 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 algebraic vector fields on smooth affine varieties.
Classification : 14H52, 17B66
Keywords: simple Lie algebras, Lie algebras of algebraic, symplectic and Hamiltonian vector fields, smooth affine curves, Danielewski surfaces, locally nilpotent derivations 
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     title = {Bracket width of simple {Lie} algebras},
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Dubouloz, Adrien; Kunyavskiĭ, Boris; Regeta, Andriy. Bracket width of simple Lie algebras. Documenta mathematica, Tome 26 (2021), pp. 1601-1627. http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a14/