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University of Colorado

1. Lamar, Jonathan P. Lattices of Supercharacter Theories.

Degree: PhD, 2018, University of Colorado

URL: https://scholar.colorado.edu/math_gradetds/60

The set of supercharacter theories of a finite group forms a lattice under a natural partial order. An active area of research in the study of supercharacter theories is the classification of this lattice for various families of groups. One other active area of research is the formation of Hopf structures from compatible supercharacter theories over indexed families of groups. This thesis therefore has two goals. First, we will classify the supercharacter theory lattice of the dihedral groups <i>D</i>_{2n} in terms of their cyclic subgroups of rotations, as well as for some semidirect products of the form ℤ<sub><i>n</i></sub> ⋊ ℤ<sub><i>p</i></sub>. Second, we will construct a pair of combinatorial Hopf algebras from natural supercharacter theories on the alternating and finite special linear groups and relate them using the theory of combinatorial Hopf algebras, as developed by Aguiar, Bergeron, and Sottile in 2006.
*Advisors/Committee Members: Nathaniel Thiem, Farid Aliniaeifard, Richard Green, Martin Walter.*

Subjects/Keywords: character theory; hopf algebras; supercharacters; semidirect product; structures; Algebra; Mathematics

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APA (6^{th} Edition):

Lamar, J. P. (2018). Lattices of Supercharacter Theories. (Doctoral Dissertation). University of Colorado. Retrieved from https://scholar.colorado.edu/math_gradetds/60

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

Lamar, Jonathan P. “Lattices of Supercharacter Theories.” 2018. Doctoral Dissertation, University of Colorado. Accessed October 30, 2020. https://scholar.colorado.edu/math_gradetds/60.

MLA Handbook (7^{th} Edition):

Lamar, Jonathan P. “Lattices of Supercharacter Theories.” 2018. Web. 30 Oct 2020.

Vancouver:

Lamar JP. Lattices of Supercharacter Theories. [Internet] [Doctoral dissertation]. University of Colorado; 2018. [cited 2020 Oct 30]. Available from: https://scholar.colorado.edu/math_gradetds/60.

Council of Science Editors:

Lamar JP. Lattices of Supercharacter Theories. [Doctoral Dissertation]. University of Colorado; 2018. Available from: https://scholar.colorado.edu/math_gradetds/60