Graduate Thesis Or Dissertation


Generalized Supercharacter Theories and Schur Rings for Hopf Algebras Public Deposited
  • 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).

Date Issued
  • 2014
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Last Modified
  • 2020-01-22
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