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HQFTs and Quantum Groups

Gupta:HQFTs and Quantum Groups

Autor:	Neha Gupta
Verfügbarkeit:	nur noch 3 lieferbar
Artikelnummer:	796280
ISBN / EAN:	9783847338574

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Autor: Neha Gupta
Verlag: LAP Lambert Academic Publishing
ISBN / EAN: 9783847338574
Bindung: Taschenbuch

Produktbeschreibung

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.