Crystallographic actions on Lie groups and post-Lie algebra structures

TL;DR

This survey explores the interplay between crystallographic groups, geometric structures on Lie groups, and related algebraic frameworks, providing insights into their mathematical relationships and classifications.

Contribution

It offers a comprehensive overview of crystallographic actions on Lie groups and introduces associated post-Lie algebra structures, synthesizing recent developments in the field.

Findings

Classification of crystallographic groups on Lie groups

Connections between geometric structures and algebraic frameworks

Insights into post-Lie algebra structures on Lie groups

Abstract

This survey on crystallographic groups, geometric structures on Lie groups and associated algebraic structures is based on a lecture given in the Ostrava research seminar in $2017$.