Degree Type

Dissertation

Date of Award

2017

Degree Name

Doctor of Philosophy

Department

Mathematics

Major

Mathematics

First Advisor

Tathagata Basak

Abstract

We exhibit a set of three related Gaussian Lorentzian lattices with ``Coxeter-like'' root diagrams. These root diagrams possess a point of symmetry in complex hyperbolic space, similar to the Weyl vector for positive-definite $\Z$-lattices. For two of the three lattices, this point of symmetry is used to show that the reflections in the diagram roots generate the lattice's reflection group. It is shown for all three lattices that the lattice's reflection group has finite index in its automorphism group.

DOI

https://doi.org/10.31274/etd-180810-5141

Copyright Owner

Jeremiah Joel Goertz

Language

en

File Format

application/pdf

File Size

76 pages

Included in

Mathematics Commons

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