  In "A note on generalized Clifford algebras and representations" (Caenepeel,
S.; Van Oystaeyen, F., Comm. Algebra 17 (1989) no. 1, 93--102.) generalized
Clifford algebras were introduced via Clifford representations; these
correspond to projective representations of a finite group (Abelian), $G$ say,
such that the corresponding twisted group ring has minimal center. The latter
then translates to the fact that the corresponding 2-cocycle allows a minimal
(none!) number of ray classes and this forces a decomposition of $G$ in cyclic
components in a suitable way, cf. Zmud, M., Symplectic geometries and
projective representations of finite Abelian groups, (Russian) Mat. Sb. (N.S.)
87(129) (1972), 3--17.. In this small paper, I will provide a way to represent
an Abelian Group Clifford Algebra using a matrix, and then give a way to
calculate whether or not the center is trivial.
