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 $p$. More specifically, we prove that there is a nice correspondence between ${\mathbb{P}}_{{\mathbb{F}}_p}^1$ and the algebras isomorphic to the quantum space ${\mathbb{C}}_{-1}[x_0,\dots ,x_{p-1}]$.

29 pages, 3 figures

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