The group of unimodular automorphisms of ${\mathbb{C}}^2$ is hopfian

Abstract

Let $G$ be the group of unimodular automorphisms of ${\mathbb{C}}^2$. In the paper we prove two interesting results about this group. The first one is about absence of non-trivial finite-dimensional representations of $G$. The second one, we show that any non-trivial group endomorphism of $G$ is a monomorphism, which implies that $G$ is hopfian.

8 pages

References in corpus (2)

• Normal subgroup generated by a plane polynomial automorphism
• Transformations birationnelles de petit degré