Open Access Senior Thesis
Bachelor of Science
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.
Arenas, Ruben, "Constructing a Matrix Representation of the Lie Group G2" (2005). HMC Senior Theses. 166.