Icosahedral Supersymmetry

Abstract

Abstract. The Exceptional Lie Algebra E 6 used by the Author as a basis for the Standard Model of the Elementary Particles is a subalgebra of the Lie algebra E 8 which in turn is the Lie algebra of the icosahedral group by the McKay correspondence.It is possible to introduce a mass proportional to an entropy given by the the number of permutations of the elements of E 6 , E 8 labeled by the Weyl group W.In this way the masses of the top-quark pair uu and electron are derived without any appeal to QCD and a mass of approximately 19 TeV is predicted for supersymmetric particles.

Icosahedral Supersymmetry and Dark Matter

“…Specifically E 12 , E 23 , E 31 are spins about x 1 , x 3 , x 2 accompanied by parities E 34 , E 24 , E 14 that are rotations about x 4 which reflect apin, while E 05 is a coordinate in isospace carrying charge. In this way equation 1covers the 12 vertices representing the nucleons and anti-nucleons on the outer shell of Fig.1 that are supposed to survive when the 6d projective space CP 3 of E 6 compactifies to a 3d projective space [5].…”

“…This letter is an appendix of the paper 'Icosahedral Supersymmetry' [5]. Essentially the Icosahedral group has the Lie algebra E 8 by the McKay cor respondence.…”

Icosahedral Symmetry and Quantum Gravity

“…The subalgebra E6 has recently been employed by de Wet [5] as a basis for the Standard Model of the elementary particles and can be described by Theta functions [2]. Furthermore representations of E8 have also been used to cover supersymmetry [4].…”