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

Abstract

Abstract We study the quadratic algebras in Artin–Schelter regular algebras of dimension 5 generated in degree 1 under the hypothesis that . 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\u2009>\u20092) Artin-Schelter regular algebras of dimension 5.