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

  • Nicolás Andruskiewitsch

    Universidad Nacional de Córdoba, Argentina; Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Córdoba, Argentina
  • Sonia Natale

    Universidad Nacional de Córdoba, Argentina; Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Córdoba, Argentina
On the finite generation of the cohomology of abelian extensions of Hopf algebras cover
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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.

Cite this article

Nicolás Andruskiewitsch, Sonia Natale, On the finite generation of the cohomology of abelian extensions of Hopf algebras. Doc. Math. (2025), published online first

DOI 10.4171/DM/1025