The collection of all projective vector fields on a Finsler space (M,F) is a finitedimensional Lie algebra with respect to the usual Lie bracket, called the projective algebra. A specific Lie sub-algebra of projective algebra of Randers spaces (called the special projective algebra) of non-zero constant S-curvature is studied and it is proved that its dimension is at most n(n+1)/2 . Moreover, a local characterization of Randers spaces whose special projective algebra has maximum dimension is established. The results uncover somehow the complexity of projective Finsler geometry versus Riemannian geometry.
