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University of Colorado

1.
Keller, Justin Charles.
Generalized Supercharacter Theories and *Schur* Rings for Hopf Algebras.

Degree: PhD, Mathematics, 2014, University of Colorado

URL: https://scholar.colorado.edu/math_gradetds/32

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 GL_{2}(q).
*Advisors/Committee Members: Nathaniel Thiem, Richard M. Green, Marty Walter, Katherine Stange, James Wilson.*

Subjects/Keywords: Hopf algebra; representation theory; Schur ring; supercharacter; Algebra; Mathematics

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APA (6^{th} Edition):

Keller, J. C. (2014). Generalized Supercharacter Theories and Schur Rings for Hopf Algebras. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/math_gradetds/32

Chicago Manual of Style (16^{th} Edition):

Keller, Justin Charles. “Generalized Supercharacter Theories and Schur Rings for Hopf Algebras.” 2014. Doctoral Dissertation, University of Colorado. Accessed October 28, 2020. https://scholar.colorado.edu/math_gradetds/32.

MLA Handbook (7^{th} Edition):

Keller, Justin Charles. “Generalized Supercharacter Theories and Schur Rings for Hopf Algebras.” 2014. Web. 28 Oct 2020.

Vancouver:

Keller JC. Generalized Supercharacter Theories and Schur Rings for Hopf Algebras. [Internet] [Doctoral dissertation]. University of Colorado; 2014. [cited 2020 Oct 28]. Available from: https://scholar.colorado.edu/math_gradetds/32.

Council of Science Editors:

Keller JC. Generalized Supercharacter Theories and Schur Rings for Hopf Algebras. [Doctoral Dissertation]. University of Colorado; 2014. Available from: https://scholar.colorado.edu/math_gradetds/32