Date of Award
Spring 1-1-2014
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics
First Advisor
Nathaniel Thiem
Second Advisor
Richard M. Green
Third Advisor
Marty Walter
Fourth Advisor
Katherine Stange
Fifth Advisor
James Wilson
Abstract
The character theory for semisimple Hopf algebras with a commutative representation ring has many similarities to the character theory of finite groups. We extend the notion of supercharacter theory to this context, and define a corresponding algebraic object that generalizes the Schur rings of the group algebra of a finite group. We show the existence of Hopf-algebraic analogues for the most common supercharacter theory constructions, specifically the wedge product and supercharacter theories arising from the action of a finite group. In regards to the action of the Galois group of the field generated by the entries of the character table, we show the existence of a unique finest supercharacter theory with integer entries, and describe the superclasses for abelian groups and the family GL2(q).
Recommended Citation
Keller, Justin Charles, "Generalized Supercharacter Theories and Schur Rings for Hopf Algebras" (2014). Mathematics Graduate Theses & Dissertations. 32.
https://scholar.colorado.edu/math_gradetds/32