Higher order Massey products for algebras over algebraic operads

Fuente: arXiv
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Main Authors: Flynn-Connolly, Oisín, Moreno-Fernández, José M.
Format: Preprint
Published: 2023
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author Flynn-Connolly, Oisín
Moreno-Fernández, José M.
author_facet Flynn-Connolly, Oisín
Moreno-Fernández, José M.
contents We introduce higher-order Massey products for algebras over algebraic operads. This extends the work of Fernando Muro on secondary ones. We study their basic properties and behavior with respect to morphisms of algebras and operads and give some connections to formality. We prove that these higher-order operations represent the differentials in a naturally associated operadic Eilenberg--Moore spectral sequence. We also study the interplay between particular choices of higher-order Massey products and quasi-isomorphic $\mathcal P_\infty$-structures on the homology of a $\mathcal P$-algebra. We focus on Koszul operads over a characteristic zero field and explain how our results generalize to the non-Koszul case.
format Preprint
id arxiv_https___arxiv_org_abs_2304_13411
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Higher order Massey products for algebras over algebraic operads
Flynn-Connolly, Oisín
Moreno-Fernández, José M.
Algebraic Topology
Rings and Algebras
18M70, 55S30, 55T20
We introduce higher-order Massey products for algebras over algebraic operads. This extends the work of Fernando Muro on secondary ones. We study their basic properties and behavior with respect to morphisms of algebras and operads and give some connections to formality. We prove that these higher-order operations represent the differentials in a naturally associated operadic Eilenberg--Moore spectral sequence. We also study the interplay between particular choices of higher-order Massey products and quasi-isomorphic $\mathcal P_\infty$-structures on the homology of a $\mathcal P$-algebra. We focus on Koszul operads over a characteristic zero field and explain how our results generalize to the non-Koszul case.
title Higher order Massey products for algebras over algebraic operads
topic Algebraic Topology
Rings and Algebras
18M70, 55S30, 55T20
url https://arxiv.org/abs/2304.13411