Date of Award

August 2017

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Allen D. Bell

Committee Members

Allen D. Bell, Craig R. Guilbault, Ian M. Musson, Jeb F. Willenbring, Yi M. Zou

Keywords

Anti-cocommutative, Connected Algebra, Enveloping Algebra, Global Dimension, HOPF Algebra, Non-commutative Algebra

Abstract

We know that given a connected Hopf algebra H, the universal enveloping algebra

U(P(H)) embeds in H as a Hopf subalgebra. Depending on P(H), we show that

there may be another enveloping algebra (not as a Hopf subalgebra) within H by

using anti-cocommutative elements. Thus, this is an extension of enveloping

algebras with regards to the Hopf structure. We also use these discoveries to apply

to global dimension, and finish with antipode behavior and future research projects.

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