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PreprintCC BY 4.0arXiv

Hochschild cohomology and AS-Gorenstein property of weak Hopf Galois extensions

  • Daowei Lu
  • Dingguo Wang
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Abstract

Let H be a weak Hopf algebra with bijective antipode. This paper is devoted to the AS-Gorenstein property of restricted faithfully flat weak H-Galois extensions A/B. We first of all study the cohomologies of weak H-Galois extensions and then establish the spectral sequence connecting the Hochschild cohomologies of A and of B. Finally we prove that when A is a noetherian affine PI algebra and B is AS-Gorenstein, A shares the AS-Gorenstein property.

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Cite

BibTeXRIS
BibTeX
@misc{lu2026hochschild,
  title = {{Hochschild cohomology and AS-Gorenstein property of weak Hopf Galois extensions}},
  author = {Daowei Lu and Dingguo Wang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.22195},
  eprint = {2608.22195},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.22195},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Hochschild cohomology and AS-Gorenstein property of weak Hopf Galois extensions
AU  - Daowei Lu
AU  - Dingguo Wang
PY  - 2026
DA  - 2026/09/02
PB  - arXiv
DO  - 10.48550/arxiv.2608.22195
UR  - https://arxiv.org/abs/2608.22195
AB  - Let H be a weak Hopf algebra with bijective antipode. This paper is devoted to the AS-Gorenstein property of restricted faithfully flat weak H-Galois extensions A/B. We first of all study the cohomologies of weak H-Galois extensions and then establish the spectral sequence connecting the Hochschild cohomologies of A and of B. Finally we prove that when A is a noetherian affine PI algebra and B is AS-Gorenstein, A shares the AS-Gorenstein property.
ER  -