Título:
Graded braided commutativity in Hochschild cohomology
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Autor:
Cóppola, Javier
Solotar, Andrea
Solotar, Andrea
Tutor:
Tipo de documento:
Preprint
Editor:
Palabras clave:
Hochschild cohomology
Nichols algebras
Hopf algebras
Braided monoidal categories
Duoidal categories
Nichols algebras
Hopf algebras
Braided monoidal categories
Duoidal categories
Descriptores:
Año de publicación:
2022
Contenido:
Resumen:
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.
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arXiv
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Financiadores:
Este trabajo ha sido financiado por los proyectos UBACYT 20020170100613BA, PIP-CONICET 11220200101855CO y Mathamsud-AREPTHEO. El primer autor mencionado recibió becas doctorales de CAP-UdelaR.
Citación:
Cóppola, J. y Solotar, A. Graded braided commutativity in Hochschild cohomology [Preprint] Publicado en : arXiv:2211.11985v1 [math.KT], nov. 2022, pp. 1-37. DOI: 10.48550/arXiv.2211.11985. https://arxiv.org/abs/2211.11985.
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Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
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| Ficheros | Descripción | Tamaño | Formato | ||
|---|---|---|---|---|---|
| CS22.pdf | Preprint | 450.09 KB | Adobe PDF |