HQFTs and Quantum Groups (Paperback)

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.

General

Imprint:	Lap Lambert Academic Publishing
Country of origin:	Germany
Release date:	2012
First published:	2012
Authors:	Neha Gupta
Dimensions:	229 x 152 x 9mm (L x W x T)
Format:	Paperback - Trade
Pages:	144
ISBN-13:	978-3-8473-3857-4
Categories:	Books > Science & Mathematics > Mathematics > General
LSN:	3-8473-3857-9
Barcode:	9783847338574

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