Gauge-Invariant Uniqueness and Reductions of Ordered Groups

Authors

Robert Huben, University of Nebraska-LincolnFollow

First Advisor

David Pitts

Second Advisor

Mark Brittenham

Date of this Version

Spring 2021

Comments

A DISSERTATION Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of Requirements For the Degree of Doctor of Philosophy, Major: Mathematics, Under the Supervision of Professors Mark Brittenham and David Pitts. Lincoln, Nebraska: May, 2021

Copyright © 2021 Robert Huben

Abstract

A reduction φ of an ordered group (G,P) to another ordered group is an order homomorphism which maps each interval [1, p] bijectively onto [1, φ(p)]. We show that if (G,P) is weakly quasi-lattice ordered and reduces to an amenable ordered group, then there is a gauge-invariant uniqueness theorem for P -graph algebras. We also consider the class of ordered groups which reduce to an amenable ordered group, and show this class contains all amenable ordered groups and is closed under direct products, free products, and hereditary subgroups.

Adviser: Mark Brittenham and David Pitts