Automorphism groups of Koras-Russell threefolds of the second kind

TL;DR

This paper determines the automorphism groups of Koras-Russell threefolds of the second kind, revealing their structure as semi-direct products and their generation by algebraic subgroups.

Contribution

It explicitly describes the automorphism groups of these threefolds, showing they are semi-direct products and generated by Gm and Ga subgroups.

Findings

Automorphism groups are semi-direct products.

Groups are generated by Gm and Ga subgroups.

Automorphism groups have a specific algebraic structure.

Abstract

We determine the automorphism groups of Koras-Russell threefolds of the second kind. In particular we show that these groups are semi-direct products of two subgroups, one given by the multiplicative group and the other isomorphic to a polynomial ring in two variables with the addition law. We also show that these groups are generated by algebraic subgroups isomorphic to Gm and Ga.