Massey products for algebras over operads

TL;DR

This paper generalizes Massey products to algebras over Koszul operads, linking them with minimal models and operadic cohomology, and provides concrete examples in Gerstenhaber and hypercommutative algebra contexts.

Contribution

It introduces a broad framework for Massey products in operadic algebras, extending classical cases and connecting to universal cohomology classes.

Findings

Defined Massey products for Koszul operad algebras in characteristic zero

Connected Massey products with minimal models and operadic cohomology

Provided explicit examples in Gerstenhaber and hypercommutative algebras

Abstract

We define a generalization of Massey products for algebras over a Koszul operad in characteristic zero, extending Massey's and Allday's and Retah's in the associative and Lie cases, respectively. We establish connections with minimal models and with Dimitrova's universal operadic cohomology class. We compute a Gerstenhaber algebra example and a hypercommutative algebra example related to the Chevalley-Eilenberg complex of the Heisenberg Lie algebra.