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

## Descriptions

Other title
Subject/Keyword

Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Rupert, Matthew
Supervisor and department
Creutzig, Thomas (Mathematical and Statistical Sciences)
Examining committee member and department
Gille, Stefan (Mathematical and Statistical Sciences)
Guay, Nicolas (Mathematical and Statistical Sciences)
Gannon, Terry (Mathematical and Statistical Sciences)
Creutzig, Thomas (Mathematical and Statistical Sciences)
Department
Department of Mathematical and Statistical Sciences
Specialization
Mathematics
Date accepted
2016-11-16T11:47:34Z
2016-06:Fall 2016
Degree
Master of Science
Degree level
Master's
Abstract
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.
Language
English
DOI
doi:10.7939/R3FQ9QH8T
Rights
This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for the purpose of private, scholarly or scientific research. 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.
Citation for previous publication
T. Creutzig, A. Milas, and M. Rupert - Logarithmic link invariants of $\overline{U}_q^H(\mathfrak{sl}(2))$ and asymptotic dimensions of singlet vertex algebras, arXiv:1605.05634

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