Browsing University Archives by Author "Ostrik, Victor"

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  • Generalized Near-Group Categories 
    Thornton, Josiah (University of Oregon, 2012)
    We give an exposition of near-group categories and generalized near-group categories. We show that both have a pseudounitary structure. We complete the classification of braided near-group categories and discuss the inherent ...
  • On Some Notions of Cohomology for Fusion Categories 
    Usher, Robert (University of Oregon, 2019-09-18)
    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 ...
  • On the Subregular J-ring of Coxeter Systems 
    Xu, Tianyuan (University of Oregon, 2017-09-06)
    Let (W, S) be an arbitrary Coxeter system, and let J be the asymptotic Hecke algebra associated to (W, S) via Kazhdan-Lusztig polynomials by Lusztig. We study a subalgebra J_C of J corresponding to the subregular cell C ...
  • Relations in the Witt Group of Nondegenerate Braided Fusion Categories Arising from the Representation Theory of Quantum Groups at Roots of Unity 
    Schopieray, Andrew (University of Oregon, 2017-09-06)
    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 ...

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