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On the monoidal invariance of the cohomological dimension of Hopf algebras

Abstract : We discuss the question of whether the global dimension is a monoidal invariant for Hopf algebras, in the sense that if two Hopf algebras have equivalent monoidal categories of comodules, then their global dimensions should be equal. We provide several positive new answers to this question, under various assumptions of smoothness, cosemisimplicity or finite dimension. We also discuss the comparison between the global dimension and the Gerstenhaber-Schack cohomological dimension in the cosemisimple case, obtaining equality in the case the latter is finite. One of our main tools is the new concept of twisted separable functor.
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https://hal.uca.fr/hal-03129963
Contributor : Julien Bichon <>
Submitted on : Tuesday, July 27, 2021 - 11:29:18 AM
Last modification on : Friday, August 13, 2021 - 3:28:15 AM

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  • HAL Id : hal-03129963, version 2
  • ARXIV : 2102.02479

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Julien Bichon. On the monoidal invariance of the cohomological dimension of Hopf algebras. 2021. ⟨hal-03129963v2⟩

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