Bookcover of HQFTs and Quantum Groups
Booktitle:

HQFTs and Quantum Groups

Homotopy Quantum Field Theory (HQFT) in dimensions two and three and Quantum Groups over group-schemes

LAP LAMBERT Academic Publishing (2012-01-13 )

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ISBN-13:

978-3-8473-3857-4

ISBN-10:
3847338579
EAN:
9783847338574
Book language:
English
Blurb/Shorttext:
The 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.
Publishing house:
LAP LAMBERT Academic Publishing
Website:
https://www.lap-publishing.com/
By (author) :
Neha Gupta
Number of pages:
144
Published on:
2012-01-13
Stock:
Available
Category:
Mathematics
Price:
59.00 €
Keywords:
quantum groups, HQFT, Crossed Systems., Quantum Groups

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