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arXiv · 2602.12731

Monoidal invariance of the cohomological dimension of Hopf algebras: the finite case

Julien Bichon
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Abstract

A consequence of the recent work of Ren and Zhu on Gorenstein projective dimensions of modules over Hopf algebras is that if $A$ and $B$ are Hopf algebras with bijective antipodes having equivalent linear tensor categories of comodules and both having finite global dimensions, then their global dimensions coincide. In this note we provide a direct proof of this result, without using Gorenstein projective dimensions, and we notice that the assumption on the bijectivity of the antipodes can be removed.

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Julien Bichon. 2026-02-13. Monoidal invariance of the cohomological dimension of Hopf algebras: the finite case. https://arxiv.org/abs/2602.12731

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