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
Copyright Date
2015
Language
en
File Format
application/pdf
File Size
71 pages
Recommended Citation
Roat, Jolie Dianna, "On 8p-dimensional Hopf algebras with the Chevalley property" (2015). Graduate Theses and Dissertations. 14618.
https://lib.dr.iastate.edu/etd/14618
