Around groups in Hilbert Geometry

TL;DR

This survey explores how groups act on Hilbert geometry, providing an overview of current knowledge and open problems in the field.

Contribution

It compiles and synthesizes existing research on group actions in Hilbert geometry, serving as a comprehensive chapter for the 'Handbook of Hilbert Geometry.'

Findings

Summarizes key results on group actions in Hilbert geometry.

Identifies open problems and future research directions.

Provides a structured overview of the field.

Abstract

This is survey about action of group on Hilbert geometry. It will be a chapter of the "Handbook of Hilbert geometry" edited by G. Besson, M. Troyanov and A. Papadopoulos.