Octonionic Cayley Spinors and E6

Details Octonionic Cayley Spinors and E6 Octonionic Cayley Spinors and E6

2009-11-11

arxiv.org/abs/0911.2255v2

Mathematics

Rings and Algebras

14 pages, 1 figure, contributed talk at 2nd Mile High Conference (Denver 2009)

Scientific paper

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.

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