Double Ore extensions versus graded skew PBW extensions

Abstract

In this article, we present necessary and sufficient conditions for a graded (trimmed) double Ore extension to be a graded (quasi-commutative) skew PBW extension. Using this fact, we prove that a graded skew PBW extension $A=\sigma (R)〈x_1,x_2〉$ of an Artin–Schelter regular algebra R is Artin–Schelter regular. As a consequence, every graded skew PBW extension $A=\sigma (R)〈x_1,x_2〉$ of a connected skew Calabi–Yau algebra R of dimension d is skew Calabi–Yau of dimension d + 2.

Keywords:

• Double Ore extensions
• graded skew PBW extensions
• Artin–Schelter regular algebras
• skew Calabi–Yau algebras

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 16W50
• 16S37
• 16W70
• 16S36
• 13N10