Degree Type

Dissertation

Date of Award

2015

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Siu-Hung Ng

Abstract

In this dissertation, we study the classification of Hopf algebras of dimension 24, and more generally, 8p where p is an odd prime. In particular, we show if a 24-dimensional Hopf algebra has a nontrivial grouplike element, then it must also have a nontrivial skew primitive element. Further, a nonsemisimple p-dimensional Hopf algebra cannot contain a semisimple Hopf subalgebra of dimension 8. Finally, we classify the nonsemisimple Hopf algebras of dimension 8p with the Chevalley property. In particular, we find such a Hopf algebra must either be pointed, or have a coradical of dimension 4p. Further the 4p-dimensional coradical can only be isomorphic to the dual of the dihedral group algebra, the dual of the dicyclic group algebra, or the self-dual, noncommutative semisimple Hopf algebra A+ of dimension 4p.

DOI

https://doi.org/10.31274/etd-180810-4170

Copyright Owner

Jolie Dianna Roat

Language

en

File Format

application/pdf

File Size

71 pages

Included in

Mathematics Commons

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