Abelian Group Clifford Algebras
Abstract
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), 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 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.
Cite
@article{arxiv.0903.4650,
title = {Abelian Group Clifford Algebras},
author = {Tim Neijens and Fred Van Oystaeyen},
journal= {arXiv preprint arXiv:0903.4650},
year = {2009}
}