Generators of Eisenstein--Picard modular group in three complex dimensions

TL;DR

This paper establishes a finite generating set for the three-dimensional Eisenstein--Picard modular group, advancing understanding of its algebraic structure in higher dimensions.

Contribution

It proves that the higher dimensional Eisenstein--Picard modular group in three complex dimensions can be generated by four specific transformations, a new result in the field.

Findings

The group is generated by four transformations.

Provides explicit generators for the group.

Advances knowledge of higher dimensional Picard modular groups.

Abstract

Little is known about the generators system of the higher dimensional Picard modular groups. In this paper, we prove that the higher dimensional Eisenstein--Picard modular group $\mathbf{PU}(3,1;\mathbb{Z}[\omega_3])$ in three complex dimensions can be generated by four given transformations.