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1. Edie-Michell, Cain. The classification of categories generated by an object of small dimension .

Degree: 2018, Australian National University

The goal of this thesis is to attempt the classification of unitary fusion categories generated by a normal object (\refi{an object comuting with its dual}{1}) of dimension less than 2. This classification has recently become accessible due to a result of Morrison and Snyder, which shows that any such category must be a cyclic extension of an adjoint subcategory of one of the ADE fusion categories. Our main tool is the classification of graded categories from , which classifies graded extensions of a fusion category in terms of the Brauer-Picard group, and Drinfeld centre of that category. We compute the Drinfeld centres, and Brauer-Picard groups of the adjoint subcategories of the ADE fusion categories. Using this information we apply the machinery of graded extensions to classify the cyclic extensions that are generated by a normal object of dimension less than 2, of the adjoint subcategories of the ADE fusion categories. Unfortunately, our classification has a gap when the dimension of the object is √{2+√{2}} corresponding to the possible existence of an interesting new fusion category. Interestingly we prove the existence of a new category, generated by a normal object of dimension 2\cos(\frac{π}{18}), which we call the DEE fusion category. We include the fusion rules for the DEE fusion categories in an appendix to this thesis.

Subjects/Keywords: Unitary fusion categories; classification; ADE

Unitary fusion categories are an important class of algebraic objects, providing a unifying… …algebras, unitary fusion categories appear as the even part of the standard invariant of a… …subfactor. Using the machinery available to unitary fusion categories, many strong results… …fusion categories [11]. For representation theory, unitary fusion categories arise as… …classification of unitary fusion categories generated by a self-dual object of dimension less than 2… 

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APA (6th Edition):

Edie-Michell, C. (2018). The classification of categories generated by an object of small dimension . (Thesis). Australian National University. Retrieved from http://hdl.handle.net/1885/146634

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Edie-Michell, Cain. “The classification of categories generated by an object of small dimension .” 2018. Thesis, Australian National University. Accessed December 05, 2020. http://hdl.handle.net/1885/146634.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Edie-Michell, Cain. “The classification of categories generated by an object of small dimension .” 2018. Web. 05 Dec 2020.

Vancouver:

Edie-Michell C. The classification of categories generated by an object of small dimension . [Internet] [Thesis]. Australian National University; 2018. [cited 2020 Dec 05]. Available from: http://hdl.handle.net/1885/146634.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Edie-Michell C. The classification of categories generated by an object of small dimension . [Thesis]. Australian National University; 2018. Available from: http://hdl.handle.net/1885/146634

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

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