A uniform approach to the simple groups of lie type
| Author | Mansoor, Abdulla Abdali Abdulla | |
|---|---|---|
| metadata.dc.contributor.department | University of Bahrain | |
| metadata.dc.date.accessioned | 2026-09-20T15:42:52Z | |
| Publication date | 2023 | |
| Degree level | Master | |
| Abstract | Abstract In this thesis we study the three simple Lie groups 𝐴, 𝐵, and 𝐺. We explore the roots system of rank 2 for these groups and the associate Lie algebra. We present the structure of the Lie algebra related to these groups graphically. We also explore the recent construction of Wilson to the groups 𝐵 and 𝐺, where he defined these groups without the use of Lie algebra. He defined these groups using their roots as a spanning set for some vector spaces and defined three types of products on those vector spaces. He then defined the groups to be the linear automorphism that preserve these products. In this thesis, the same approach will be applied to the simple case of 𝐴, where many of the procedures in Wilson’s paper will be naturally augmented to 𝐴 as these groups are all from the same family as simple groups of Lie type with root system of dimension 2. | ملخص في هذه الرسالة نناقش زمر لي الثلاث والتي لا تحتوي على زمر جزئية عادية. وستشمل المناقشة نظام الجذور من الرتبة الثانية لهذه الزمر. سترتكز هذه الدراسة على طريقة ويلسون في تعريف هذه الزمر باستخدام الفضاءات المولدة التي تحافظ على أنواع معينة من عمليات الضرب وبدون استخدام النظريات المتعلقة بجبريات لي. وسيتم استخدام نفس الطريقة لتعريف جميع زمر لي بنفس المنهجية المتبعة من ويلسون . | |
| metadata.dc.identifier.other | Drupal node 1072 | |
| metadata.dc.identifier.other | https://digitalrepository.uob.edu.bh/en/dar/uniform-approach-simple-groups-lie-type | |
| metadata.dc.identifier.uri | http://165.227.56.122/handle/123456789/6018 | |
| Language | en | |
| Link | https://digitalrepository.uob.edu.bh/en/_flysystem/fedora/2024-08/abdulla-abdali-abdulla-mansoor.pdf | |
| Subject | Lie groups -- Dissertations | |
| Subject | Group theory -- dissertations | |
| Title | A uniform approach to the simple groups of lie type | |
| Type | Master's Thesis |
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