Massey products and higher operations

Abstract

It was long believed that Massey products in the cohomology of a differential graded associative algebra were determined by the higher operations on a minimal A-infinity model. This was disproved by Buijs, Moreno-Fernández, and Murillo. They also gave sufficient conditions for it to hold. In this talk, we will present two further conditions:

- Associative algebras with sparse cohomology.

- Algebras over Koszul operads.

In the latter case, we define an analogue of triple Massey products which extends the cases previously considered in the literature (associative and Lie algebras).