The Exceptional Lie Algebra E_{6} used by the Author as a basis forthe 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 toan 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.

Periodical:

International Frontier Science Letters (Volume 2)

Pages:

52-54

DOI:

10.18052/www.scipress.com/IFSL.2.52

Citation:

J.A. de Wet "Icosahedral Supersymmetry", International Frontier Science Letters, Vol. 2, pp. 52-54, 2014

Online since:

Oct 2014

Authors:

Keywords:

Distribution:

Open Access

This work is licensed under a

Creative Commons Attribution 4.0 International License

References:

J.F. Adams, Lectures on Exceptional Lie Groups, The University of Chicago Press, (1996).

W. Barth and I. Nieto, Abelian surfaces of type (1, 3) and quartic surfaces with 16 skew lines, J. Algebraic Geometry 3 (1994) 173-222.

H,S.M. Coxeter, The polytope 221 where 27 vertices corespond to the lines on the general cubic surface, American J. of Mathematics, 62 (1940) 457-486.

H.S.M. Coxeter, Regular Complex Polytopes, 2nd ed., Cambridge Univer- sity Press, (1991).

J.A. de Wet, A group theoretical approach to the many nucleon problem, Proc. Camb. Phil. Soc., 70 (1971)485-496.

J. A, de Wet, Icosahedral symmetry in the MSSM, Int. Mathematical Forum, 3(2008)777282, (Available on-line at Hikari Ltd).

J.A. de Wet, A Standard Model algebra, Int. Mathematical Forum, 7(2012)49-52.

J.A. de Wet, On the strong force without QCD, Int. Mathematical Forum, 7(2012)129-132.

J.A. de Wet, Particle knots in Toric Modular Space, Bulletin of Society for Mathematical Services @ Standards, 3(2014)54-59.

Bruce Hunt, The Geometry of some Arithmetic Quotients, Lecture Notes in Mathematics , 1637, Springer(1996).

L. Manivel, Configuration of lines and models of Lie algebras, arXiv; math. AG/0507118.

R. Slansky, Group Theory for Unified Model Building, Unity of Forces in Universe, Ed.A. Lee, World Scientific, (1992).