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

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