Graduate Thesis Or Dissertation

 

Generalized Supercharacter Theories and Schur Rings for Hopf Algebras Public Deposited

https://scholar.colorado.edu/concern/graduate_thesis_or_dissertations/qf85nb29f
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).

Creator
Date Issued
  • 2014
Academic Affiliation
Advisor
Committee Member
Degree Grantor
Commencement Year
Subject
Last Modified
  • 2020-01-22
Resource Type
Rights Statement
Language

Relationships

Items