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

2024/07/08 by Nicolás Andruskiewitsch, Andruskiewitsch, Nicolás, Sonia Natale +1 · 1 citation
Mathematics · #16T05 #17B37 #18M05 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2407.05881

openalex publication_date 2024/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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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