Séminaires : Séminaire d'Algèbre

A poset is said to be fractionally Calabi-Yau if the bounded derived category of its incidence algebra over a field is fractionally Calabi-Yau. In other words, a power of the Serre functor is isomorphic to a shift. When going from a poset to its derived category, one looses almost all the combinatorics of the poset. However in some favorable cases, part of the combinatorics is encoded in the Serre functor.

In this talk, I will present the combinatorics of the Serre functor of the Tamari lattice. This leads to a more algebraic proof of its fractional Calabi-Yau property. It is also the first step toward a generalization to a larger family of posets. 

This talk will take place in hybrid mode at the Institut Henri Poincaré.