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With the aim of derive a quasi-monomiality formulation in the context ofdiscrete hypercomplex variables, one will amalgamate through aClifford-algebraic structure of signature $(0,n)$ the umbral calculus frameworkwith 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 loweringoperators acting on the lattice $h\BZ^n$ is used to derive the correspondinghypercomplex polynomials of discrete variable as Appell sets with membership onthe space Clifford-vector-valued polynomials. Some particular examplesconcerning this construction such as the hypercomplex versions of fallingfactorials and the Poisson-Charlier polynomials are introduced. Certainapplications from the view of interpolation theory and integral transforms arealso discussed.

Classes of hypercomplex polynomials of discrete variable based on the quasi-monomiality principle