Date of Award
Fall 2023
Project Type
Dissertation
Program or Major
Mathematics
Degree Name
Doctor of Philosophy
First Advisor
Dmitri Nikshych
Second Advisor
Maria Basterra
Third Advisor
Orly Buchbinder
Abstract
Fusion categories are generalizations of finite groups and are found in areas of mathematics that involve algebraic structures. They are also found in other fields, such as theoretical physics (quasiparticles) and computer science (quantum computing). Their ubiquitousness in these areas make them useful subjects to study.
As a generalization of finite groups, fusion category theory contains many analogs to the objects and constructions found in group theory. But an analog to an essential object of study in group theory, that of the quotient group, is relatively unexplored. In this work, we introduce quotients of braided fusion categories as certain hypergroups associated with fusion subcategories. We then define a new canonical structure associated to a fusion category, called a central hypergroup. We show that for a large class of braided fusion categories, the central hypergroup takes on an integral form.
Recommended Citation
Hempel, Alice A., "Hypergroups From Fusion Subcategories and Their Integral Forms" (2023). Doctoral Dissertations. 2786.
https://scholars.unh.edu/dissertation/2786