Graded Clifford Algebras of Prime Global Dimension with an Action of H (p)

Abstract

In this article, we study graded Clifford algebras with a gradation preserving action of automorphisms given by H-p, the Heisenberg group of order p(3) with p prime. After reviewing results in dimensions 3 and 4, we will determine the graded Clifford algebras that are AS-regular algebras of global dimension 5 and generalize certain results to arbitrary dimension p.