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arXiv · 1810.06778

Double Ore extensions versus graded skew PBW extensions

James Yair Gómez·Héctor Suárez
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Abstract

In this paper 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 $A = σ(R)\langle x_1,x_2 \rangle$ of an Artin-Schelter regular algebra $R$ is Artin-Schelter regular. As a consequence, every graded skew PBW extension $A = σ(R)\langle x_1,x_2 \rangle$ of a connected skew Calabi-Yau algebra $R$ of dimension $d$ is skew Calabi-Yau of dimension $d+2$.

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James Yair Gómez, Héctor Suárez. 2018-10-16. Double Ore extensions versus graded skew PBW extensions. https://arxiv.org/abs/1810.06778

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