Dirac Spinor: 4 component object that transforms under boost and rotations according to a Ki, Ji matrices.

The most important finite dimensional almost irreducible rep of L+ is the dirac spinor.
if {Gu,Gn}=anticommutator=-2nuv (a dirac algebra) => Sun=i/4[Gu,Gn].

Gu's are 4x4 matrices.
G0=

        O I2
        I2 0

Gi=

        0  Si
        -Si 0

Ki=S0i=i/4*[G0,Gi]= -i/2*

        Si 0
        0 -Si

Ji= .5*eijk Sjk= .5*

        Si 0
        0 Si