A Family of Complex Kleinian Split Solvable Groups
Waldemar Barrera, Rene Garcia, Juan Pablo Navarrete

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.
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Taxonomy
Topicsadvanced mathematical theories · Molecular spectroscopy and chirality · Topological and Geometric Data Analysis
