Free quadri-algebras and dual quadri-algebras

Loïc Foissy (1)

1 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville

We study quadri-algebras and dual quadri-algebras. We describe the free quadri-algebra on one generator as a subobject of the Hopf algebra of permutations FQSym, proving a conjecture due to Aguiar and Loday, using that the operad of quadri-algebras can be obtained from the operad of dendriform algebras by both black and white Manin products. We also give a combinatorial description of free dual quadri-algebras. A notion of quadri-bialgebra is also introduced, with the applications to the Hopf algebras FQSym and WQSym.

Mots clés: Koszul duality; Combinatorial Hopf algebras; Quadri-algebras

Domaines: Anneaux et algèbres [math.RA]

Loïc Foissy. Free quadri-algebras and dual quadri-algebras. Communications in Algebra, 2020, 48 (12), pp.5123-5141. ⟨10.1080/00927872.2020.1779736⟩. ⟨hal-01082289⟩