A conformal group approach to the Dirac-Kahler system on the lattice

Starting from the representation of the (n-1)+n-dimensional Lorentz pseudo-sphere on the projective space PRn,n, we propose a method to derive a class of solutions underlying to a Dirac-Kahler type equation on the lattice. We make use of the Cayley transform phi(w) to show that the resulting group representation arises from the same mathematical framework as the conformal group representation in terms of the general linear groupGL(n-1,n-1){0}. That allows us to describe such class of solutions as a commutative n-ary product, involving the quasi-monomials phi with membership in the paravector space R circle plus Rejen+j. Copyright (c) 2016 John Wiley & Sons, Ltd.