Noetherian Connected Graded Algebras of Global Dimension 3

Darin R. Stephenson and James J. Zhang

email: stephenson@hope.edu, zhang@math.washington.edu

Abstract: Let A be a noetherian connected graded algebra of global dimension 3. We show that A is regular in the sense of Artin and Schelter if one of the following conditions holds:

  1. A is generated by 2 elements
  2. the graded simple module has a standard resolution
  3. the degrees of the minimal relations are the same (this includes the quadratic case)
Some general properties of A are studied without assuming regularity.
Darin R. Stephenson (stephenson@hope.edu)