Let be a Hopf algebra and be an -module algebra. This article investigates when the smash product is (skew) Calabi–Yau, has Van den Bergh duality or is Artin–Schelter regular or Gorenstein. In particular, if and are skew Calabi–Yau, then so is and its Nakayama automorphism is expressed using the ones of and . This is based on a description of the inverse dualising complex of when is a homologically smooth dg algebra and is homologically smooth and with invertible antipode. This description is also used to explain the compatibility of standard constructions of Calabi–Yau dg algebras with taking smash products.
Cite this article
Patrick Le Meur, Smash products of Calabi–Yau algebras by Hopf algebras. J. Noncommut. Geom. 13 (2019), no. 3, pp. 887–961DOI 10.4171/JNCG/341