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arXiv · 2608.22195

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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Daowei Lu, Dingguo Wang. 2026-08-23. Hochschild cohomology and AS-Gorenstein property of weak Hopf Galois extensions. https://arxiv.org/abs/2608.22195

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