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Exotic Fusion Categories and Their Modular Data

  • Author / Creator
    Budinski, Paul Garrett
  • The majority of known examples of fusion categories come directly from classical structures -- vector spaces, groups, representations, and the like. In recent years the technique of constructing fusion categories as endomorphisms on Cuntz algebras was developed and has already lead to completely new examples of fusion categories. Somewhat surprisingly, the fusion categories found seem to belong to infinite families. We push the Cuntz construction further and find more examples within two potentially infinite families, the near group fusion categories and the Haagerup-Izumi fusion categories. For all of the newly cataloged fusion categories, we also compute their modular data. In the case of the Haagerup-Izumi series, we find that all new examples satisfy the conjecture of \\cite{GannonHg}, which posits an unexpectedly simple form for the modular data in terms of certain bilinear forms. In the case of near group categories associated to an odd ordered abelian group, we find that the modular data of new examples also satisfy a similar conjecture (found in \\cite{GannonNG}). When the order of the group is even, no such conjecture existed; we provide a new conjecture which predicts the modular data for all current examples.

  • Subjects / Keywords
  • Graduation date
    Fall 2021
  • Type of Item
    Thesis
  • Degree
    Master of Science
  • DOI
    https://doi.org/10.7939/r3-7p7k-fg18
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.