{"product_id":"hqfts-and-quantum-groups-homotopy-quantum-field-theory-hqft-in-dimensions-two-and-three-and-quantum-groups-over-group-schemes-von-neha-gupta","title":"HQFTs and Quantum Groups","description":"\u003cp\u003eThe 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 äne case and conjectured for non-äne 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.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783847338574\"\u003e\u003ch3\u003eHomotopy Quantum Field Theory (HQFT) in dimensions two and three and Quantum Groups over group-schemes\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9783847338574","offer_id":39451369472093,"sku":"9783847338574","price":59.0,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/6932fd6f-2ce9-4c28-b901-dd89ec78a329.jpg?v=1746691124","url":"https:\/\/shop.autorenwelt.de\/products\/hqfts-and-quantum-groups-homotopy-quantum-field-theory-hqft-in-dimensions-two-and-three-and-quantum-groups-over-group-schemes-von-neha-gupta","provider":"Autorenwelt Shop","version":"1.0","type":"link"}