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You searched for +publisher:"University of Colorado" +contributor:("James Wilson"). Showing records 1 – 2 of 2 total matches.

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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

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). 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 · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th 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 (16th Edition):

Keller, Justin Charles. “Generalized Supercharacter Theories and Schur Rings for Hopf Algebras.” 2014. Doctoral Dissertation, University of Colorado. Accessed October 30, 2020. https://scholar.colorado.edu/math_gradetds/32.

MLA Handbook (7th Edition):

Keller, Justin Charles. “Generalized Supercharacter Theories and Schur Rings for Hopf Algebras.” 2014. Web. 30 Oct 2020.

Vancouver:

Keller JC. Generalized Supercharacter Theories and Schur Rings for Hopf Algebras. [Internet] [Doctoral dissertation]. University of Colorado; 2014. [cited 2020 Oct 30]. 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


University of Colorado

2. Andrews, Scott D. Type-free Approaches to Supercharacter Theories of Unipotent Groups.

Degree: PhD, Mathematics, 2014, University of Colorado

Supercharacter theories are a relatively new tool in studying the representation theory of unipotent groups over finite fields. In this thesis I present two new approaches to constructing supercharacter theories of finite unipotent groups. The first method utilizes group actions to construct supercharacter theories of the unipotent orthogonal, symplectic and unitary groups. The second technique is via the method of little groups, which describes the irreducible characters of a semidirect product with an abelian normal subgroup in terms of the irreducible characters of the factor groups. Motivated by these constructions, I produce supercharacter theories for a large collection of unipotent matrix groups and construct a Hopf monoid on the supercharacters. Advisors/Committee Members: Nathaniel Thiem, Richard M. Green, Sebastian Casalaina-Martin, Martin Walter, James Wilson.

Subjects/Keywords: combinatorics; representation theory; supercharacter; unipotent group; Discrete Mathematics and Combinatorics; Mathematics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Andrews, S. D. (2014). Type-free Approaches to Supercharacter Theories of Unipotent Groups. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/math_gradetds/31

Chicago Manual of Style (16th Edition):

Andrews, Scott D. “Type-free Approaches to Supercharacter Theories of Unipotent Groups.” 2014. Doctoral Dissertation, University of Colorado. Accessed October 30, 2020. https://scholar.colorado.edu/math_gradetds/31.

MLA Handbook (7th Edition):

Andrews, Scott D. “Type-free Approaches to Supercharacter Theories of Unipotent Groups.” 2014. Web. 30 Oct 2020.

Vancouver:

Andrews SD. Type-free Approaches to Supercharacter Theories of Unipotent Groups. [Internet] [Doctoral dissertation]. University of Colorado; 2014. [cited 2020 Oct 30]. Available from: https://scholar.colorado.edu/math_gradetds/31.

Council of Science Editors:

Andrews SD. Type-free Approaches to Supercharacter Theories of Unipotent Groups. [Doctoral Dissertation]. University of Colorado; 2014. Available from: https://scholar.colorado.edu/math_gradetds/31

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