Bialgebra cohomology and exact sequences

2023/09/19 by Julien Bichon, Bichon, Julien
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT) #Nonlinear Waves and Solitons #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.2309.10434

openalex publication_date 2023/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show how the bialgebra cohomologies of two Hopf algebras involved in an exact sequence are related, when the third factor is finite-dimensional cosemisimple. As an application, we provide a short proof of the computation of the bialgebra cohomology of the universal cosovereign Hopf algebras in the generic (cosemisimple) case, done recently by Baraquin, Franz, Gerhold, Kula and Tobolski.

Citations

• On Finite-Dimensional Semisimple and Cosemisimple Hopf Algebras in Positive Characteristic
• Hopf Modules and Yetter - Drinfel′d Modules

Related

• Bialgebra cohomology, pointed Hopf algebras, and deformations
• Cyclic Cohomology of Hopf algebras and Hopf Algebroids
• Cosemisimple Hopf algebras with antipode of arbitrary finite order
• Cohomological dimensions of universal cosovereign Hopf algebras
• Lazy cohomology: an analogue of the Schur multiplier for arbitrary Hopf algebras