# Smash products of Calabi–Yau algebras by Hopf algebras

@article{Meur2015SmashPO, title={Smash products of Calabi–Yau algebras by Hopf algebras}, author={Patrick Le Meur}, journal={Journal of Noncommutative Geometry}, year={2015} }

Let H be a Hopf algebra and A be an H-module algebra. This article investigates when the smash product A#H is (skew) Calabi-Yau, has Van den Bergh duality or is Artin-Schelter regular or Gorenstein. In particular, if A and H are skew Calabi-Yau, then so is A#H and its Nakayama automorphism is expressed using the ones of A and H. This is based on a description of the inverse dualising complex of A#H when A is a homologically smooth dg algebra and H is homologically smooth and with invertible…

## 4 Citations

### Skew Calabi-Yau property of normal extensions

- Mathematicsmanuscripta mathematica
- 2018

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…

### Skew Calabi-Yau property of normal extensions

- Mathematicsmanuscripta mathematica
- 2018

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…

### A note on the bijectivity of the antipode of a Hopf algebra and its applications

- MathematicsProceedings of the American Mathematical Society
- 2018

Certain sufficient homological and ring-theoretical conditions are given for a Hopf algebra to have bijective antipode with applications to noetherian Hopf algebras regarding their homological…

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