  With the aim of derive a quasi-monomiality formulation in the context of
discrete hypercomplex variables, one will amalgamate through a
Clifford-algebraic structure of signature $(0,n)$ the umbral calculus framework
with Lie-algebraic symmetries. The exponential generating function ({\bf EGF})
carrying the {\it continuum} Dirac operator $D=\sum_{j=1}^n\e_j\partial_{x_j}$
together with the Lie-algebraic representation of raising and lowering
operators acting on the lattice $h\BZ^n$ is used to derive the corresponding
hypercomplex polynomials of discrete variable as Appell sets with membership on
the space Clifford-vector-valued polynomials. Some particular examples
concerning this construction such as the hypercomplex versions of falling
factorials and the Poisson-Charlier polynomials are introduced. Certain
applications from the view of interpolation theory and integral transforms are
also discussed.
