  We define a superalgebra S2(N/2) as a Z2 graded algebra of dimension 2N+3,
where N is a positive, odd integer. The even component is a three-dimensional
abelian subalgebra, while the odd component is made up of two N-dimensional,
mutually conjugate algebras. For N = 1, two of the three even elements become
identical, resulting in a four-dimensional superalgebra which is the graded
extension of the SO(2,1) Lie algebra that has recently been introduced in the
solution of the Dirac equation for spinn 1/2. Realization of the elements of
S2(N/2) is given in terms of differential matrix operators acting on an N+1
dimensional space that could support a representation of the Lorentz space-time
symmetry group for spin N/2. The N = 3 case results in a 4x4 matrix wave
equation, which is linear and of first order in the space-time derivatives. We
show that the "canonical" form of the Dirac Hamiltonian is an element of this
superalgebra.
