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The thesis is divided into two parts one for dimension 2 and the other for dimension 3. Part one of the thesis generalizes the de¿nition 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 generalization of Turaev's theory into a purely categorical set-up. Part two of the thesis generalizes the concept of a group-coalgebra, Hopf group-coalgebra, crossed Hopf group-coalgebra and quasitriangular Hopf group-coalgebra over a group scheme. Quantum double of a crossed Hopf group-scheme coalgebra is constructed in the äne case and conjectured for non-äne 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. Hence generates 3-dimensional HQFTs under certain conditions if the category becomes modular. However, systematic ¿nding of modular crossed G-categories is largely open.
| Autorius: | Neha Gupta |
| Leidėjas: | LAP Lambert Academic Publishing |
| Išleidimo metai: | 2016 |
| Knygos puslapių skaičius: | 144 |
| ISBN-10: | 3847338579 |
| ISBN-13: | 9783847338574 |
| Formatas: | 220 x 150 x 10 mm. Knyga minkštu viršeliu |
| Kalba: | Anglų |
Parašykite atsiliepimą apie „HQFTs and Quantum Groups: Homotopy Quantum Field Theory (HQFT) in dimensions two and three and Quantum Groups over group-schemes“
