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arXiv · 2501.02828

Artin-Schelter Gorenstein property of Hopf Galois extensions

Ruipeng Zhu
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Abstract

This paper investigates the homological properties of the faithfully flat Hopf Galois extension $A \subseteq B$. It establishes that when $B$ is a noetherian affine PI algebra and $A$ is AS Gorenstein, $B$ inherits the AS Gorenstein property. Furthermore, we demonstrate that injective dimension serves as a monoidal invariant for AS Gorenstein Hopf algebras. Specifically, if two such Hopf algebras have equivalent monoidal categories of comodules, then their injective dimensions are equal.

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Ruipeng Zhu. 2025-01-06. Artin-Schelter Gorenstein property of Hopf Galois extensions. https://arxiv.org/abs/2501.02828

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