Constructing a Matrix Representation of the Lie Group G2

Author

Ruben Arenas, Harvey Mudd College

Graduation Year

2005

Document Type

Open Access Senior Thesis

Degree Name

Bachelor of Science

Department

Mathematics

Reader 1

Weiqing Gu

Reader 2

Vatche Sahakian

Abstract

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.

Recommended Citation

Arenas, Ruben, "Constructing a Matrix Representation of the Lie Group G2" (2005). HMC Senior Theses. 166.
https://scholarship.claremont.edu/hmc_theses/166