Anthony Réveillac (INSA Toulouse)
Niels Kowalzig (Università di Napoli Federico II)
In this talk, we will give an overview of how typical ingredients of cyclic homology theories and (algebraic) operads naturally appear when looking for (higher) brackets on certain cohomology groups, like Gerstenhaber brackets in Hochschild cohomology. More precisely, we will explain how the notion of cyclic operad with multiplication is related to BV algebras, that is, Gerstenhaber algebras the bracket of which can be expressed in terms of a cup product and Connes' cyclic coboundary. Examples are given by the cohomology groups for Hopf algebras with involutive antipode (or even Hopf algebroids) or the Hochschild cohomology of Frobenius and Calabi-Yau algebras.
No prior knowledge on operads is required to follow the talk.