Skew Calabi-Yau property of normal extensions

2017/09/27 by Zhou, G. -S., Shen, Y., Lu, D. -M. · 2 citations
#14A22 #16E65 #16S20 #16W50 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1709.09292

Abstract

We prove that the skew Calabi-Yau property is preserved under normal extension for locally finite positively graded algebras. We also obtain a homological identity which describes the relationship between the Nakayama automorphisms of skew Calabi-Yau locally finite positively graded algebras and their normal extensions. As a preliminary, we show that the Nakayama automorphisms of skew Calabi-Yau algebras always send a regular normal element to a multiple of itself by a unit.

Cited by

• Quiver down-up algebras
• The structure of iterated Hopf Ore extensions

Related

• Skew Calabi-Yau property of faithfully flat Hopf Galois extensions
• Nakayama automorphism of quasi-commutative skew PBW extensions over AS-regular algebras
• Nakayama automorphisms of double Ore extensions of Koszul regular algebras
• Commonly Graded Algebras and Their Homological Properties
• Twisted Calabi-Yau property of Ore extensions