This thesis was concerned with classifying the real indecomposable solvable Lie algebras with codimension one nilradicals of dimensions two through seven. This thesis was organized into three chapters.
In the first, we described the necessary concepts and definitions about Lie algebras as well as a few helpful theorems that are necessary to understand the project. We also reviewed many concepts from linear algebra that are essential to the research.
The second chapter was occupied with a description of how we went about classifying the Lie algebras. In particular, it outlined the basic premise of the classification: that we can use the automorphisms of the nilradical of the Lie algebra to find a basis with the simplest structure equations possible. In addition, it outlined a few other methods that also helped find this basis. Finally, this chapter included a discussion of the canonical forms of certain types of matrices that arose in the project.
The third chapter presented a sample of the classification of the seven-dimensional Lie algebras. In it, we proceeded step-by-step through the classification of the Lie algebras whose nilradical was one of four specifically chosen because they were representative of the different types that arose during the project.
In the appendices, we presented our results in a list of the multiplication tables of the isomorphism classes found.
| Identifer | oai:union.ndltd.org:UTAHS/oai:digitalcommons.usu.edu:etd-8245 |
| Date | 01 May 2007 |
| Creators | Parry, Alan R. |
| Publisher | DigitalCommons@USU |
| Source Sets | Utah State University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | All Graduate Theses and Dissertations |
| Rights | Copyright for this work is held by the author. Transmission or reproduction of materials protected by copyright beyond that allowed by fair use requires the written permission of the copyright owners. Works not in the public domain cannot be commercially exploited without permission of the copyright owner. Responsibility for any use rests exclusively with the user. For more information contact digitalcommons@usu.edu. |
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