  By exploring a spinor space whose elements carry a spin 1/2 representation of
the Lorentz group and satisfy the the Fierz-Pauli-Kofink identities we show
that certain symmetries operations form a Lie group. Moreover, we discuss the
reflex of the Dirac dynamics in the spinor space. In particular, we show that
the usual dynamics for massless spinors in the spacetime is related to an
incompressible fluid behavior in the spinor space.
