  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.
