What is evolutionary significance of archeae?

The three-domain system divides the cellular life forms into archaea, bacteria, and eukaryote domains. The evolutionary relationship between the three domains is of central importance for understanding the origin of life.

This study had revealed that most of the metabolic pathways, which comprise the majority of an organism's genes, are common between Archaea and Bacteria, while most genes involved in genome expression are common between Archaea and Eukaryotes.

The evolutionary relationship between archaea and eukaryotes has not been extensively studied still and if you have a thirst for knowledge in this field, you are encouraged..!