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arXiv · 1401.7800

Graded Clifford algebras of prime global dimension with an action of H_p

Kevin De Laet
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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 $\mathbb{P}^1_{\mathbb{F}_p}$ and the algebras isomorphic to the quantum space $\mathbb{C}_{-1}[x_0,\ldots,x_{p-1}]$.

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Kevin De Laet. 2014-06-11. Graded Clifford algebras of prime global dimension with an action of H_p. https://doi.org/10.1080/00927872.2014.942423

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