Reprint of: Linearity and nonlinearity of groups of polynomial automorphisms of the plane.

Given a field K , we investigate which subgroups of the group Aut A K 2 of polynomial automorphisms of the plane are linear or not. The results are contrasted. The group Aut A K 2 itself is nonlinear, except if K is finite, but it contains some large subgroups, of "codimension-five" or more, which are linear. This phenomenon is specific to dimension two: it is easy to prove that any natural "finite-codimensional" subgroup of Aut A K 3 is nonlinear, even for a finite field K. When ch K = 0 , we also look at a similar questions for f.g. subgroups, and the results are again disparate. The group Aut A K 2 has a one-related f.g. subgroup which is not linear. However, there is a large subgroup, of "codimension-three", which is locally linear but not linear. [ABSTRACT FROM AUTHOR]