Hqfts and Quantum Groups: Homotopy Quantum Field Theory (Hqft) in Dimensions Two and Three and Quantum Groups over Group-schemes - Neha Gupta - Bøger - LAP LAMBERT Academic Publishing - 9783847338574 - 13. januar 2012
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Hqfts and Quantum Groups: Homotopy Quantum Field Theory (Hqft) in Dimensions Two and Three and Quantum Groups over Group-schemes

Neha Gupta

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Hqfts and Quantum Groups: Homotopy Quantum Field Theory (Hqft) in Dimensions Two and Three and Quantum Groups over Group-schemes

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 a?ne case and conjectured for non-a?ne 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.

Medie Bøger     Paperback Bog   (Bog med blødt omslag og limet ryg)
Udgivet 13. januar 2012
ISBN13 9783847338574
Forlag LAP LAMBERT Academic Publishing
Antal sider 144
Mål 150 × 9 × 226 mm   ·   222 g
Sprog Engelsk  

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