Sur une opérade ternaire liée aux treillis de Tamari

Frédéric Chapoton (1)

1 ICJ - Institut Camille Jordan

We introduce an anticyclic operad V given by a ternary generator and a quadratic relation. We show that it admits a natural basis indexed by planar binary trees. We then relate this construction to the familly of Tamari lattices (Y_n) for n>=0 by defining an isomorphism between V(2n+1) and the Grothendieck group of the category mod Y_n. This isomorphism maps the basis of V(2n+1) to the classes of projective modules and sends the anticyclic map of the operad V to the Coxeter transformation of the derived category of mod Y_n.

Mots clés: operad; Dendriform operad; anticyclic operad; ternary operad; binary tree; Tamari lattice; Coxeter transformation

Domaines: Algèbres quantiques [math.QA]

Frédéric Chapoton. Sur une opérade ternaire liée aux treillis de Tamari. 2011. ⟨hal-00578227v1⟩