Mathematische Zeitschrift· 2026Q1
Higher-order Massey products for algebras over algebraic operads
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- Q1SCImago
- 2026year
Short summary
Higher-order Massey products are introduced for algebras over algebraic operads, extending prior work on secondary Massey products.
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Key points
- Introduced higher-order Massey products for algebras over algebraic operads.
- Studied basic properties and behavior with respect to morphisms.
- Established connections to formality.
- Proved these operations represent differentials in an operadic Eilenberg–Moore spectral sequence.
- Investigated interplay with P∞-structures and homology of P-algebras.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract 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 $$\mathcal {P}_\infty $$ P ∞ -structures on the homology of a $$\mathcal {P}$$ P -algebra. We focus on Koszul operads over a characteristic zero field and indicate how our results generalize to the non-Koszul case.
The authors' abstract, as published at the source. Mathematische Zeitschrift, 2026 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics