Logarithmic Hopf Link Invariants for the Unrolled Restricted Quantum Group of sl(2)

• Author / Creator

  Rupert, Matthew

• Little is known about Vertex Operator Algebras (VOAs) which are neither semi-simple nor rational, and most of the work on such VOAs has been focused around specific examples such as the Singlet VOA. In this thesis, the relationship between subcategories of the module categories of the Singlet VOA and the unrolled restricted quantum group associated to sl(2) at 2r-th root of unity is studied. A family of deformable modules is used to efficiently compute open Hopf links and particular (1,1)-tangle invariants colored with projective modules of the quantum group. These tangle invariants are extensions of the Alexander invariants defined by Murakami. It is also shown that normalized modified traces of open Hopf links for modules of the unrolled restricted quantum group of sl(2) correspond exactly with the asymptotic quantum dimensions for certain modules of the Singlet.

• Subjects / Keywords

  • Unrolled
  • Algebra
  • Group
  • Logarithmic
  • Link
  • Sl(2)
  • Restricted
  • Operator
  • Singlet
  • Quantum
  • Vertex
  • Verlinde
  • Hopf
  • Invariant
  • Sl2

• Graduation date

  Fall 2016

• Type of Item

  Thesis

• Degree

  Master of Science

• DOI

  https://doi.org/10.7939/R3FQ9QH8T

• 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.