Geometry of Majorana neutrino and new symmetries
  Experimental observation of Majorana fermion matter gives a new impetus to the understanding of the Lorentz symmetry and its extension, the geometrical properties of the ambient space-time structure, matter--antimatter symmetry and some new ways to understand the baryo-genesis problem in cosmology. Based on the primordial Majorana fermion matter assumption, we discuss a possibility to solve the baryo-genesis problem through the the Majorana-Diraco genesis in which we have a chance to understand creation of Q(em) charge and its conservation in our D=1+3 Universe after the Big Bang. In the Majorana-Diraco genesis approach there appears a possibility to check the proton and electron non-stability on the very low energy scale. In particle physics and in our space-time geometry, the Majorana nature of the neutrino can be related to new types of symmetries which are lying beyond the binary Cartan-Killing-Lie algebras/superalgebras. This can just support a conjecture about the non-completeness of the SM in terms of binary Cartan--Killing--Lie symmetries/supersymmetries. As one of the very important applications of such new ternary symmetries could be related with explanation of the nature of the three families and three colour symmetry. The Majorana neutrino can directly indicate the existence of a new extra-dimensional geometry and thanks to new ternary space-time symmetries, could lead at high energies to the unextraordinary phenomenological consequences. 
G.G. Volkov