Octonionic geometry and conformal transformations

Abstract

We describe space-time using split octonions over the reals and use their group of automorphisms, the noncompact form of Cartan’s exceptional Lie group G2, as the main geometrical group of the model. Connections of the G2-rotations of octonionic 8D space with the conformal transformations in 4D Minkowski space-time are studied. It is shown that the dimensional constant needed in these analysis naturally gives the observed value of the cosmological constant.