A Family of Complex Kleinian Split Solvable Groups

TL;DR

This paper demonstrates that certain split solvable subgroups of PSL(N+1,C) have lattices that act as complex Kleinian groups, revealing their limit sets and discontinuity regions through Lie group and dynamical systems methods.

Contribution

It introduces a new family of split solvable groups with complex Kleinian lattice actions, detailing their limit sets and discontinuity regions.

Findings

Lattices of these groups are complex Kleinian.

Existence of a minimal limit set for the lattice action.

Exactly two maximal discontinuity regions identified.

Abstract

It is shown that lattices of a family of split solvable subgroups of PSL(N + 1, C) are complex Kleinian using techniques of Lie groups and dynamical systems, also that there exists a minimal limit set for the action of these lattices on the N dimensional complex projective space and that there are exactly two maximal discontinuity regions.