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Braided Hopf algebras and non-trivially associated tensor categories. / Mohammed Mosa Al-Shomrani

Swansea University Author: Mohammed Mosa Al-Shomrani

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...

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Published: 2003
Institution: Swansea University
Degree level: Doctoral
Degree name: Ph.D
URI: https://cronfa.swan.ac.uk/Record/cronfa42794
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first_indexed 2018-08-02T18:55:33Z
last_indexed 2018-08-03T10:11:07Z
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spelling 2018-08-02T16:24:30.5077956 v2 42794 2018-08-02 Braided Hopf algebras and non-trivially associated tensor categories. 5b420af86b098baf79f924cffe7ebcbf NULL Mohammed Mosa Al-Shomrani Mohammed Mosa Al-Shomrani true true 2018-08-02 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 &isin; C, using this j)artial braiding. Finally, ideas for further research are included. E-Thesis Mathematics. 31 12 2003 2003-12-31 COLLEGE NANME Mathematics COLLEGE CODE Swansea University Doctoral Ph.D 2018-08-02T16:24:30.5077956 2018-08-02T16:24:30.5077956 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Mohammed Mosa Al-Shomrani NULL 1 0042794-02082018162522.pdf 10807570.pdf 2018-08-02T16:25:22.4100000 Output 4447293 application/pdf E-Thesis true 2018-08-02T16:25:22.4100000 false
title Braided Hopf algebras and non-trivially associated tensor categories.
spellingShingle Braided Hopf algebras and non-trivially associated tensor categories.
Mohammed Mosa Al-Shomrani
title_short Braided Hopf algebras and non-trivially associated tensor categories.
title_full Braided Hopf algebras and non-trivially associated tensor categories.
title_fullStr Braided Hopf algebras and non-trivially associated tensor categories.
title_full_unstemmed Braided Hopf algebras and non-trivially associated tensor categories.
title_sort Braided Hopf algebras and non-trivially associated tensor categories.
author_id_str_mv 5b420af86b098baf79f924cffe7ebcbf
author_id_fullname_str_mv 5b420af86b098baf79f924cffe7ebcbf_***_Mohammed Mosa Al-Shomrani
author Mohammed Mosa Al-Shomrani
author2 Mohammed Mosa Al-Shomrani
format E-Thesis
publishDate 2003
institution Swansea University
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 1
active_str 0
description 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 &isin; C, using this j)artial braiding. Finally, ideas for further research are included.
published_date 2003-12-31T03:53:40Z
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score 11.035655

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