Geodesic
Nonsimplicity of the group of unimodular automorphisms of the affine plane
Matematičeskie zametki, Tome 15 (1974) no. 2, pp. 289-293.

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It is proven that the group of automorphisms of the affine plane (as an algebraic manifold), with Jacobian equal to 1, is not simple. 
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     author = {V. I. Danilov},
     title = {Nonsimplicity of the group of unimodular automorphisms of the affine plane},
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V. I. Danilov. Nonsimplicity of the group of unimodular automorphisms of the affine plane. Matematičeskie zametki, Tome 15 (1974) no. 2, pp. 289-293. http://geodesic.mathdoc.fr/item/MZM_1974_15_2_a14/