Geodesic
Graded braided commutativity in Hochschild cohomology
Theory and applications of categories, Tome 41 (2024), pp. 1596-1643.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

We prove the graded braided commutativity of the Hochschild cohomology of A with trivial coefficients, where A is a braided Hopf algebra in the category of Yetter-Drinfeld modules over the group algebra of an abelian group, under some finiteness conditions on a projective resolution of A as A-bimodule. This is a generalization of a result by Mastnak, Pevtsova, Schauenburg and Witherspoon to a context which includes Nichols algebras such as the Jordan and the super Jordan plane. We prove this result by constructing a coduoid-up-to-homotopy structure on the aforementioned projective resolution in the duoidal category of chain complexes of A-bimodules. We also prove that the Hochschild complex of a braided bialgebra A in an arbitrary braided monoidal category is a cocommutative comonoid up to homotopy with the deconcatenation product which induces the cup product in Hochschild cohomology.
Publié le :
Classification : 16B50, 16E40, 18G35, 18M15.
Keywords: Hochschild cohomology, Nichols algebras, Hopf algebras, braided monoidal categories, duoidal categories 
@article{TAC_2024_41_a45,
     author = {Javier C\'oppola and Andrea Solotar},
     title = {Graded braided commutativity in {Hochschild} cohomology},
     journal = {Theory and applications of categories},
     pages = {1596--1643},
     publisher = {mathdoc},
     volume = {41},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2024_41_a45/}
}
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Javier Cóppola; Andrea Solotar. Graded braided commutativity in Hochschild cohomology. Theory and applications of categories, Tome 41 (2024), pp. 1596-1643. http://geodesic.mathdoc.fr/item/TAC_2024_41_a45/