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Title: Braided Hopf algebras and non-trivially associated tensor categories
Author: Al-Shomrani, Mohammed Mosa
Awarding Body: University of Wales, Swansea
Current Institution: Swansea University
Date of Award: 2003
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The rigid non-trivially associated tensor category C is constructed from left coset representatives M of a subgroup G of a finite group X. There is also a braided category D made from C by a double construction. In this thesis we consider some basic useful facts about D, including the fact that it is a modular category (modulo a matrix being invertible). Also we give a definition of the character of an object in this category as an element of a braided Hopf algebra in the category. The definition is shown to be adjoint invariant and multiplicative. A detailed example is given. Next we show an equivalence of categories between the non-trivially associated double D and the trivially associated category of representations of the double of the group D(X). Moreover, we show that the braiding for D extends to a partially defined braiding on C, and also we look at an algebra A ∈ C, using this j)artial braiding. Finally, ideas for further research are included.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available