  We study some algebraic properties of the 'vector supersymmetry' (VSUSY)
algebra, a graded extension of the four-dimensional Poincare' algebra with two
odd generators, a vector and a scalar, and two central charges. The
anticommutator between the two odd generators gives the four-momentum operator,
from which the name vector supersymmetry. We construct the Casimir operators
for this algebra and we show how both algebra and Casimirs can be derived by
contraction from the simple orthosymplectic algebra OSp(3,2|2). In particular,
we construct the analogue of superspin for vector supersymmetry and we show
that, due to the algebraic structure of the Casimirs, the multiplets are either
doublets of spin (s,s+1) or two spin 1/2 states. Finally, we identify an odd
operator, which is an invariant in a subclass of representations where a
BPS-like algebraic relation between the mass and the values of the central
charges is satisfied.

High Energy Physics - Theory