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Description
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.
Spécifications
Parties prenantes
- Auteur(s) :
- Editeur:
Contenu
- Nombre de pages :
- 144
- Langue:
- Anglais
Caractéristiques
- EAN:
- 9783847338574
- Date de parution :
- 13-01-12
- Format:
- Livre broché
- Format numérique:
- Trade paperback (VS)
- Dimensions :
- 152 mm x 229 mm
- Poids :
- 222 g
