Higher order Massey products for algebras over algebraic operads
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916120198381568 |
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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 |