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arXiv · 2407.05881

On the finite generation of the cohomology of abelian extensions of Hopf algebras

Nicolás Andruskiewitsch·Sonia Natale
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Abstract

A finite-dimensional Hopf algebra is called quasi-split if it is Morita equivalent to a split abelian extension of Hopf algebras. Combining results of Schauenburg and Negron, it is shown that every quasi-split finite-dimensional Hopf algebra satisfies the finite generation cohomology conjecture of Etingof and Ostrik. This is applied to a family of pointed Hopf algebras in odd characteristic introduced by Angiono, Heckenberger and the first author, proving that they satisfy the aforementioned conjecture.

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Nicolás Andruskiewitsch, Sonia Natale. 2024-07-08. On the finite generation of the cohomology of abelian extensions of Hopf algebras. https://arxiv.org/abs/2407.05881

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