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OverviewThe thesis is divided into two parts one for dimension 2 and the other for dimension 3. Part one of the thesis generalizes 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 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 affine case and conjectured for 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. Hence generates 3-dimensional HQFTs under certain conditions if the category becomes modular. However, systematic finding of modular crossed G-categories is largely open. Full Product DetailsAuthor: Neha Gupta (Northeastern University USA)Publisher: LAP Lambert Academic Publishing Imprint: LAP Lambert Academic Publishing Dimensions: Width: 15.20cm , Height: 0.90cm , Length: 22.90cm Weight: 0.222kg ISBN: 9783847338574ISBN 10: 3847338579 Pages: 144 Publication Date: 13 January 2012 Audience: General/trade , General Format: Paperback Publisher's Status: Active Availability: In stock  We have confirmation that this item is in stock with the supplier. It will be ordered in for you and dispatched immediately. Table of ContentsReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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