Conjugacy classes of special automorphisms of the affine spaces
  In the group of polynomial automorphisms of the plane, the conjugacy class of an element is closed if and only if the element is diagonalisable. In this article, we show that this does not hold for the group of special automorphisms, giving then a first step towards the direction of showing that this group is not simple, as an infinite-dimensional algebraic group. 
J\'er\'emy Blanc
math.AG