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Homotopy quantum field theory and quantum groups
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Gupta, Neha, 1982- (2011) Homotopy quantum field theory and quantum groups. PhD thesis, University of Warwick.
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Official URL: http://webcat.warwick.ac.uk/record=b2533293~S1
Abstract
The thesis is divided into two parts one for dimension 2 and the other for dimension 3. Part one (Chapter 3) of the thesis generalises the definition of an n-dimensional HQFT in terms of a monoidal functor from a rigid symmetric monoidal category X-Cobn to any monoidal category A. In particular, 2-dimensional HQFTs with target K(G,1) taking values in A are generated from any Turaev G-crossed system in A and vice versa. This is the generalisation of the theory given by Turaev into a purely categorical set-up. Part two (Chapter 4) of the thesis generalises the concept of a group-coalgebra, Hopf group-coalgebra, crossed Hopf group-coalgebra and quasitriangular Hopf group-coalgebra in the case of a group scheme. Quantum double of a crossed Hopf group-scheme coalgebra is constructed in the affine case and conjectured for the more general non-affine case. We can construct 3-dimensional HQFTs from modular crossed G-categories. The category of representations of a quantum double of a crossed Hopf group-coalgebra is a ribbon (quasitriangular) crossed group-category, and hence can generate 3-dimensional HQFTs under certain conditions if the category becomes modular. However, the problem of systematic finding of modular crossed G-categories is largely open.
| Item Type: | Thesis or Dissertation (PhD) |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Library of Congress Subject Headings (LCSH): | Quantum field theory |
| Date: | February 2011 |
| Institution: | University of Warwick |
| Theses Department: | Mathematics Institute |
| Thesis Type: | PhD |
| Publication Status: | Unpublished |
| Supervisor(s)/Advisor: | Rumynin, Dmitriy, 1971- |
| Sponsors: | University of Warwick |
| Extent: | 196 leaves : ill. |
| Language: | eng |
| URI: | http://wrap.warwick.ac.uk/id/eprint/38110 |
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