Bialgebraic approach to rack cohomology - Normandie Université Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2019

Bialgebraic approach to rack cohomology

Simon Covez
  • Fonction : Auteur
  • PersonId : 872604
Marco Farinati
  • Fonction : Auteur

Résumé

We interpret the complexes defining rack cohomology in terms of a certain differential graded bialgebra. This yields elementary algebraic proofs of old and new structural results for this cohomology theory. For instance, we exhibit two explicit homotopies controlling structure defects on the cochain level: one for the commutativity defect of the cup product, and the other one for the "Zinbielity" defect of the dendriform structure. We also show that, for a quandle, the cup product on rack cohomology restricts to, and the Zinbiel product descends to quandle cohomology. Finally, for rack cohomology with suitable coefficients, we complete the cup product with a compatible coproduct.

Dates et versions

hal-02140507 , version 1 (27-05-2019)

Identifiants

Citer

Simon Covez, Marco Farinati, Victoria Lebed, Dominique Manchon. Bialgebraic approach to rack cohomology. 2019. ⟨hal-02140507⟩
64 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More