The purpose of this thesis is to give a classification of anisotropic algebraic groups over number fields of higher real rank. This will complete the classification of algebraic groups over number fields of higher real rank, which was begun by V. Chernousov, L. Lifschitz and D.W. Morris in their paper "Almost-Minimal Non-Uniform Lattices of Higher Rank''. The classification of anisotropic groups of higher real rank is also used to provide a classification of uniform lattices of higher rank contained in semisimple Lie groups with no compact factors. In particular, it is shown that all such lattices sit inside Lie groups of type An.
This thesis proceeds as follows: The first chapter provides motivation for the classification and introduces all the main results of the thesis. The second chapter provides relevant definitions and background material for the proof. The next chapters provide a proof of the classification theorem, with chapters 3-5 examining the absolutely simple groups and the final chapter examining the simple groups which are not absolutely simple. / Mathematics
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:AEU.10048/1001 |
| Date | 06 1900 |
| Creators | Ondrus, Alexander A. |
| Contributors | Chernousov, Vladimir (Mathematical and Statistical Sciences), Pianzola, Arturo (Mathematical and Statistical Sciences), Kuttler, Jochen (Mathematical and Statistical Sciences), Cliff, Gerald (Mathematical and Statistical Sciences), Penin, Alexander (Physics), Garibaldi, Skip, Emory University (Mathematics and Computing Science) |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 1069600 bytes, application/pdf |
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