The quadratic algebras in Artin-Schelter regular algebras of dimension five

Abstract

We study the quadratic algebras in Artin–Schelter regular algebras of dimension 5 generated in degree 1 under the hypothesis that $\text{GKdim}\ge 4$. All the algebras obtained are proved to be Koszul algebras or piecewise-Koszul algebras. In addition, we find that there don’t exist d-Koszul (d > 2) Artin-Schelter regular algebras of dimension 5.

Keywords:

• Artin–Schelter regular algebra
• d-Koszul algebra
• Koszul algebra
• piecewise-Koszul algebra
• quadratic algebra

2000 Mathematics Subject Classifications:

• 16E40
• 16S37
• 16W50

Additional information

Funding

The research is supported by the HNNSF (Grant No. 2018JJ3586).