Finite groups acting on Severi-Brauer surfaces

TL;DR

This paper classifies finite groups that can act on Severi-Brauer surfaces via automorphisms and birational automorphisms over fields of characteristic zero, enhancing understanding of their symmetry properties.

Contribution

It provides a complete classification of finite groups acting on non-trivial Severi-Brauer surfaces, a problem not previously fully addressed.

Findings

Identifies all finite groups acting on Severi-Brauer surfaces

Distinguishes automorphism and birational automorphism groups

Advances understanding of surface symmetries in algebraic geometry

Abstract

We classify finite groups that can act by automorphisms and birational automorphisms on non-trivial Severi-Brauer surfaces over fields of characteristic zero.