We define the Lie group G2 and show several equivalent ways to view G2. We do the same with its Lie algebra g2. We identify a new basis for g2 using Bryant’s view of g2 and geometric considerations we develop. We then show how to construct a matrix representation of G2 given our particular basis for g2. We examine the geometry of 1 and 2-parameter subgroups of G2. Finally, we suggest an area of further research using the new geometric characterization we developed for g2.
| Identifer | oai:union.ndltd.org:CLAREMONT/oai:scholarship.claremont.edu:hmc_theses-1169 |
| Date | 01 May 2005 |
| Creators | Arenas, Ruben |
| Publisher | Scholarship @ Claremont |
| Source Sets | Claremont Colleges |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | HMC Senior Theses |
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