Bracket width of Lie algebras of vector fields on affine curves

We study Lie algebras of vector fields on smooth affine curves with a trivial tangent bundle.  These Lie algebras consist of multiples of one derivation and are simple. It was proven by A. Dubouloz, B. Kunyavskii and A. Regeta that the bracket width of such an algebra is strictly greater than one if the curve is not rational and has a unique place at infinity. We prove that the bracket widths of Lie algebras of vector fields on smooth affine curves with a trivial tangent bundle are less than or equal to 3, and less than or equal to 2 if the curve is planar. So we construct examples of simple Lie algebras with bracket width equal to 2.

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https://us02web.zoom.us/j/87856132062

Meeting ID: 878 5613 2062