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We introduce higher-order Massey products for algebras over algebraicoperads. This extends the work of Fernando Muro on first-order ones. We studytheir basic properties and behavior with respect to morphisms of algebras andoperads and give some connections to formality. We prove that thesehigher-order secondary operations represent the differentials in a naturallyassociated operadic Eilenberg--Moore spectral sequence. We also study theinterplay between particular choices of higher-order Massey products andquasi-isomorphic $\mathcal P_\infty$-structures on the homology of a $\mathcalP$-algebra. We focus on Koszul operads over a characteristic zero field andexplain how our results generalize to the non-Koszul case.

Higher order Massey products for algebras over algebraic operads