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Journal Articles Communications in Algebra Year : 2020

Free quadri-algebras and dual quadri-algebras


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.
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hal-01082289 , version 1 (13-11-2014)





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⟩
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