Bialgebra cohomology and exact sequences
Julien Bichon (LMBP)
TL;DR
This paper explores the relationship between bialgebra cohomologies of Hopf algebras in exact sequences, providing new proofs and insights into their structure, especially for universal cosovereign Hopf algebras in the cosemisimple case.
Contribution
It establishes a connection between the bialgebra cohomologies of Hopf algebras in an exact sequence with a finite-dimensional cosemisimple third factor, and offers a simplified proof for a recent cohomology computation.
Findings
Relation between bialgebra cohomologies in exact sequences
Simplified proof for cohomology of universal cosovereign Hopf algebras
Extension of cohomology computation to cosemisimple cases
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.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Nonlinear Waves and Solitons