Simple subgroups of the real space Cremona group

TL;DR

This paper classifies finite simple non-abelian subgroups of the real three-dimensional Cremona group, identifying only the alternating groups A5 and A6 as such subgroups.

Contribution

It proves that A5 and A6 are the only finite simple non-abelian subgroups of the real 3D Cremona group, providing a complete classification.

Findings

A5 and A6 are the only finite simple non-abelian subgroups

The classification is complete for the real 3D Cremona group

No other finite simple non-abelian groups are subgroups

Abstract

We show that the alternating groups $\mathfrak{A}_5$ and $\mathfrak{A}_6$ are the only finite simple non-abelian subgroups of the group of birational selfmaps of the real three-dimensional projective space.