The existence of the Majorana fermion matter gives the further
development in the study of the external space-time symmetries,
i.e. Lorentz symmetry and new symmetries beyond its.
These new symmetries can help us to understand the ambient geometry
of our world and   to observe new space-time properties of neutrino.
The new space-time symmetries can lead to the superluminal
velocity of neutrino at high energies which can be checked at
CERN-Gran-Sasso neutrino experiments.