On Some Notions of Cohomology for Fusion Categories

dc.contributor.advisor	Ostrik, Victor
dc.contributor.author	Usher, Robert
dc.date.accessioned	2019-09-18T19:22:50Z
dc.date.available	2019-09-18T19:22:50Z
dc.date.issued	2019-09-18
dc.description.abstract	In this dissertation, we study two main topics: superfusion categories, and embeddings of symmetric fusion categories into modular fusion categories. Using a construction of Brundan and Ellis, we give a formula relating the fermionic 6$j$-symbols of a superfusion category to the 6$j$-symbols of the corresponding underlying fusion category, and prove a version of Ocneanu rigidity for superfusion categories. Inspired by the work of Lan, Kong, and Wen on the group of modular extensions of a symmetric fusion category, we also give definitions for the low cohomology groups of a finite supergroup and show these definitions are functorial. This dissertation includes previously published material.	en_US
dc.identifier.uri	https://hdl.handle.net/1794/24886
dc.language.iso	en_US
dc.publisher	University of Oregon
dc.rights	All Rights Reserved.
dc.subject	Modular extensions	en_US
dc.subject	Superfusion categories	en_US
dc.title	On Some Notions of Cohomology for Fusion Categories
dc.type	Electronic Thesis or Dissertation
thesis.degree.discipline	Department of Mathematics
thesis.degree.grantor	University of Oregon
thesis.degree.level	doctoral
thesis.degree.name	Ph.D.

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