Octonionic Cayley Spinors and E6

Abstract

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.

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

References in corpus (1)

• The Structure of E6

Cited by in corpus (5)

• Octonions, E6, and Particle Physics
• The genetic code, 8-dimensional hypercomplex numbers and dyadic shifts
• Time, E8, and the Standard Model
• Matrix mechanics of the relativistic point particle and string in Clifford space
• Constructing Quantum Mechanics from a Clifford substructure of the relativistic point particle