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Logarithmic Parafermion Vertex Operator Algebras

  • Author / Creator
    Auger, Jean
  • This thesis is about the theory of vertex operator algebras and their representations. Its main results provide new examples of logarithmic C2-cofinite vertex operator algebras. These include closure of the characters under modular transformations with explicit determination of the modular coefficients for an infinite family of parafermionic vertex operator algebras and proofs of C2-cofiniteness for a few specific levels including for three new cases. The rest of the work presented in this thesis provides a new comprehension of the notoriously difficult proof of the Kac-Wakimoto character formula, but also categorical results and tools to study certain vertex operator algebras' categories involving infinite direct sums.

  • Subjects / Keywords
  • Graduation date
    Fall 2018
  • Type of Item
    Thesis
  • Degree
    Doctor of Philosophy
  • DOI
    https://doi.org/10.7939/R3FF3MG26
  • License
    Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.