  Utilizing Lie superalgebra (LS) realizations via the Relative Parabose Set
algebra $P_{BF}$, combined with earlier results on the Fock-like
representations of $P_{BF}^{(1,1)}$, we proceed to the construction of a family
of Fock-like representations of LSs: these are infinite dimensional,
decomposable super-representations, which are parameterized by the value of a
positive integer $p$. They can be constructed for any LS $L$, either initiating
from a given 2-dimensional, $\mathbb{Z}_{2}$-graded representation of $L$ or
using its inclusion as a subalgebra of $P_{BF}^{(1,1)}$. As an application we
proceed in studying decompositions with respect to various low-dimensional Lie
algebras and superalgebras.
