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.

Key Words:

• Graded Clifford algebras
• Heisenberg group
• Quantum spaces

2010 Mathematics Subject Classification:

• 16W20

ACKNOWLEDGMENTS

The author would like to thank M. Van den Bergh, who proposed to look at these algebras and who has been a tremendous help along the way, and L. le Bruyn, who gave ideas on what to do with these algebras and who also gave tips on how to write a readable paper. The author would also like to thank T. Raedschelders for suggesting to include a section with preliminaries.

Notes

Communicated by T. Lenagan.