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Braided Hopf algebras and non-trivially associated tensor categories. / Mohammed Mosa Al-Shomrani
Swansea University Author: Mohammed Mosa Al-Shomrani
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Abstract
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 i...
| Published: |
2003
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| Institution: | Swansea University |
| Degree level: | Doctoral |
| Degree name: | Ph.D |
| URI: | https://cronfa.swan.ac.uk/Record/cronfa42794 |
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| Abstract: |
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. |
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| Keywords: |
Mathematics. |
| College: |
Faculty of Science and Engineering |