Quid of deformations of algebras over operads.

par Saikat Goswami (TCG Crest)

mercredi 25 mars 2026, 18:00 → 20:00 Europe/Paris

207, Salle Pellos. (1R2, IMT)

In the jungle of non-associative algebras, each algebra seems to come with its own tools and techniques. For instance, deformations of algebraic structures are controlled by a deformation complex that appears to vary from algebra to algebra. In particular, deformation of associative algebras is governed by the Hochschild complex, commutative algebras by the Harrison complex, and Lie algebras by the Chevalley-Eilenberg complex. However, losing some local details, if one manages to get a bird's-eye view, a common pattern appears. It turns out that these algebras speak in a common language, the language of algebraic operads. 

In this talk, I aim to introduce the notion of algebraic operads and explain how these apparently different-looking deformation complexes arise as a particular instance of a single cochain complex associated with the underlying operads of these algebras.