%0 Journal Article
%T Octonionic Cayley Spinors and E6
%A Tevian Dray
%A Corinne A. Manogue
%J Mathematics
%D 2009
%I arXiv
%X Attempts to extend our previous work using the octonions to describe fundamental particles lead naturally to the consideration of a particular real, noncompact form of the exceptional Lie group E6, and of its subgroups. We are therefore led to a description of E6 in terms of 3x3 octonionic matrices, generalizing previous results in the 2x2 case. Our treatment naturally includes a description of several important subgroups of E6, notably G2, F4, and (the double cover of) SO(9,1), An interpretation of the actions of these groups on the squares of 3-component "Cayley spinors" is suggested.
%U http://arxiv.org/abs/0911.2255v2