Séminaires : Séminaire d'Algèbre

Cambrian lattices originate in the theory of Coxeter groups. They appear as 1-skeletons of generalised associahedra or as lattices of torsion classes of representation finite hereditary algebras. Rognerud has shown that Cambrian lattices of linear type A, better known as Tamari lattices, are fractionally Calabi-Yau. That is a power of the Serre functor on the derived category of their incidence algebra agrees with a power of the shift.
The m-cluster categories are an m+1 Calabi-Yau version of cluster categories. They contain a family of m-cluster tilting objects connected by a notion of mutation. In this talk I will introduce a family of intervals in crystallographic Cambrian lattices that exhibit the same combinatorics as 2-cluster tilting objects in 2-cluster categories. As a consequence I will show that Cambrian lattices are fractionally Calabi-Yau.

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