Journal of Noncommutative Geometry


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Volume 8, Issue 2, 2014, pp. 587–609
DOI: 10.4171/JNCG/165

Published online: 2014-07-18

Twisted Calabi–Yau property of Ore extensions

Liyu Liu[1], Shengqiang Wang[2] and Quanshui Wu[3]

(1) Fudan University, Shanghai, China
(2) Fudan University, Shanghai, China
(3) Fudan University, Shanghai, China

Suppose that $E=A[x;\sigma,\delta]$ is an Ore extension with $\sigma$ an automorphism. It is proved that if $A$ is twisted Calabi–Yau of dimension $d$, then $E$ is twisted Calabi–Yau of dimension $d+1$. The relation between their Nakayama automorphisms is also studied. As an application, the Nakayama automorphisms of a class of 5-dimensional Artin–Schelter regular algebras are given explicitly.

Keywords: Ore extension, twisted Calabi–Yau algebra, Nakayama automorphism, Artin–Schelter regular algebra

Liu Liyu, Wang Shengqiang, Wu Quanshui: Twisted Calabi–Yau property of Ore extensions. J. Noncommut. Geom. 8 (2014), 587-609. doi: 10.4171/JNCG/165