One-Parameter Homogeneous Differential Realization and Boson–Fermion Realization of the SPL(2,1) Superalgebra

One-parameter homogeneous differential realization of the SPL(2,1) superalgebra on the space of homogeneous polynomials and the corresponding boson–fermion realization are studied. The parameter α may be related to the interaction parameter U in one exactly solvable model for correlated electrons.