On 8p-dimensional Hopf algebras with the Chevalley property
Date
Authors
Major Professor
Advisor
Committee Member
Journal Title
Journal ISSN
Volume Title
Publisher
Altmetrics
Authors
Research Projects
Organizational Units
Journal Issue
Is Version Of
Versions
Series
Department
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.