Construction of Exceptional Lie Algebra G2 and Non-Associative Algebras using Clifford Algebra
Greg Wilmot -- University of Adelaide
This article uses Geometric algebra to derive octonions and the Lie exceptional algebra G2 from calibrations. This is simpler than the usual exterior algebra derivation and uncovers an invertible element using the calibrations that is used to classify six other algebras which are found to be related to the symmetries of G2. The 4-form calibration terms are a subalgebra of Spin(7) and provide a direct construction of G2 for each of the 480 representations of the octonions. This result is extended to 15 dimensions, deriving another 93 algebras including the sedenions.