Finite group actions on curves of genus zero

TL;DR

This paper classifies finite group actions on genus zero curves by analyzing subgroups of algebraic groups of type A1 over various fields, providing a comprehensive understanding of their structure.

Contribution

It offers a complete classification of finite subgroups of algebraic groups of type A1 over arbitrary fields, extending previous results to a broader context.

Findings

Classification of finite subgroups up to conjugacy

Analysis over arbitrary fields of characteristic not 2

Extension of known results to new algebraic settings

Abstract

We classify, up to conjugacy, the finite (constant) subgroups G of adjoint absolutely simple algebraic groups of type $A_1$ over an arbitrary field $k$ of characteristic not 2.