Characterization of New Algebras Resembling Colour Algebras based on Split-Octonion units in the Classification of Hadronic Symmetries and Supersymmetries

Abstract

We report on some new algebras we discovered that does not appear in mathematics or physics literature which we briefly name “R” algebras. Together with the real forms we developed for supersting theories shown below and dobbed as “l” algebras, both these new algebras seem to imitate split-octonionic multiplication rules we expose below. We further elaborate on Jordan algebras, magic squares, seven spheres, and supergravity, pointing to the existence of a larger theory with a 27-dimensional lattice and unifying all known superstring theories.