We shall start by introducing a Poincar Group P,which contains the generators and , these which must enable the relations
to be satisfied. (Eq. 1)

There should also be an internal symmetry group S, with its own generators in order to satisfy
.(Eq. 2)

One essential procedure in formulating supersymmetric algebra is to introduce generators that are anti-commutative:
. (Eq. 3)
"i" and are actually indices. We also still must retain the relations . (Eq. 4)

As a consequence of the relations (Eq.5), we find that the commutator between and , have to be
(Eq. 6)
as are all odd.
In a Lie algebra, there are Jacobi identities. If we represent an even generator by A, and a odd generator by B, then
. (Eq. 7)
All these relations are identical.

When we use (Eq. 8) on (Eq. 9) would mean
.(Eq. 10)
would represent the Lorentz Group.
By selecting to be in (Eq. 11)
representing the Lorentz Group.
Choosing to be a Majorana spinor:
(Eq. 12)
is the charge conjugation matrix. The commutator of an even generator, and will be
(Eq. 13).
With the generalized Jacobi Identity, it means that
(Eq. 14)
This would also mean that
(Eq. 15)
(Eq. 16) is a representation of the Lie algebra of the internal symmetry group. There is, however, still a odd-even generator [, P_a ]. It is possible that the Lorentz Group and the internal symmetry group permit
.(Eq. 17)

There is also one last anti-commutator: .(Eq. 18) Being a term( made up of generators that are even )that is symmetric when a exchange between the material equivalent and , and also between and , a possibility would be
.(Eq. 19)

Let us introduce a supercharge: , and also consider the commutator of both generator of the internal symmetry group & the supercharge. (Eq. 15) would transform into:
(Eq. 20)
Multiplying by the Dirac conjugate,
.(Eq. 21)
By using (Eq. 12),
. (Eq. 22)
Using the Jacobi Identity,
. (Eq. 23)
Final result is:
. (Eq. 24)

The N=1 Supersymmetry algebra is :
. (Eq. 25)

Basically, one can formulate a simple N=1 Supersymmetry algebra by grading the algebra and retaining relations. A Poincare group and an internal symmetry group, when contained, the Jacobi identities will constraint algebra. One can also take it that the introduced generators( ) are spinors under the Lorentz group.