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Journal Article

Bracket width of simple Lie algebras


Kunyavskiĭ,  Boris
Max Planck Institute for Mathematics, Max Planck Society;


Regeta,  Andriy
Max Planck Institute for Mathematics, Max Planck Society;

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Dubouloz, A., Kunyavskiĭ, B., & Regeta, A. (2021). Bracket width of simple Lie algebras. Documenta Mathematica, 26, 1601-1627. doi:10.25537/dm.2021v26.1601-1627.

Cite as: https://hdl.handle.net/21.11116/0000-000C-C4E1-8
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 discov-
ered 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 algebraic
vector fields on smooth affine varieties.