On the finite generation of the cohomology of abelian extensions of Hopf algebras
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.
Authors
- Nicolás Andruskiewitsch (ORCID: https://orcid.org/0000-0002-9163-5161)
- Sonia Natale (ORCID: https://orcid.org/0000-0001-9888-979X)
Institutions
- Consejo Nacional de Investigaciones Científicas y Técnicas (AR)
- Universidad Nacional de Córdoba (AR)
- Centro Científico Tecnológico - Córdoba (AR)
Publication Details
- Journal
- Documenta Mathematica
- Published
- 2025-08-28
- DOI
- https://doi.org/10.4171/dm/1025
- Citations
- 1
- Primary Topic
- Algebraic structures and combinatorial models
- Type
- article
- Field-Weighted Citation Impact
- 4.09
Funders
- Consejo Nacional de Investigaciones Científicas y Técnicas
- Southern University of Science and Technology
- Agencia Nacional de Promoción Científica y Tecnológica
- Fondo para la Investigación Científica y Tecnológica