Relations in the Witt Group of Nondegenerate Braided Fusion Categories Arising from the Representation Theory of Quantum Groups at Roots of Unity
| dc.contributor.advisor | Ostrik, Victor | |
| dc.contributor.author | Schopieray, Andrew | |
| dc.date.accessioned | 2017-09-06T21:41:50Z | |
| dc.date.available | 2017-09-06T21:41:50Z | |
| dc.date.issued | 2017-09-06 | |
| dc.description.abstract | For each finite dimensional Lie algebra $\mathfrak{g}$ and positive integer $k$ there exists a modular tensor category $\mathcal{C}(\mathfrak{g},k)$ consisting of highest weight integrable $\hat{\mathfrak{g}}$-modules of level $k$ where $\hat{\mathfrak{g}}$ is the corresponding affine Lie algebra. Relations between the classes $[\mathcal{C}(\mathfrak{sl}_2,k)]$ in the Witt group of nondegenerate braided fusion categories have been completely described in the work of Davydov, Nikshych, and Ostrik. Here we give a complete classification of relations between the classes $[\mathcal{C}(\mathfrak{sl}_3,k)]$ relying on the classification of conncted \'etale alegbras in $\mathcal{C}(\mathfrak{sl}_3,k)$ ($SU(3)$ modular invariants) given by Gannon. We then give an upper bound on the levels for which exceptional connected \'etale algebras may exist in the remaining rank 2 cases ($\mathcal{C}(\mathfrak{so}_5,k)$ and $\mathcal{C}(\mathfrak{g}_2,k)$) in hopes of a future classification of Witt group relations among the classes $[\mathcal{C}(\mathfrak{so}_5,k)]$ and $[\mathcal{C}(\mathfrak{g}_2,k)]$. This dissertation contains previously published material. | en_US |
| dc.identifier.uri | https://hdl.handle.net/1794/22630 | |
| dc.language.iso | en_US | |
| dc.publisher | University of Oregon | |
| dc.rights | All Rights Reserved. | |
| dc.subject | Quantum algebra | en_US |
| dc.subject | Representation Theory | en_US |
| dc.title | Relations in the Witt Group of Nondegenerate Braided Fusion Categories Arising from the Representation Theory of Quantum Groups at Roots of Unity | |
| 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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