Free algebraic structures on the permutohedra

JOURNAL OF ALGEBRA

卷:487

Article

Burgunder, Emily¹  Curien, Pierre-Louis²  Ronco, Maria³ 

[1] Univ Paul Sabatier, Inst Math Toulouse, 118 Route Narbonne, F-31062 Toulouse 9, France

[2] CNRS, UMR 7126, Lab PPS, F-31062 Paris 9, France

[3] Univ Talca, IMAFI, Campus Norte,Avda Lircay S-N, Talca, Chile

关键词: Bialgebras;    Dendriform;    Surjective maps;   

DOI  :  10.1016/j.jalgebra.2016.05.016

来源: Elsevier

【 摘 要 】

Tridendriform algebras are a type of associative algebras, introduced independently by F. Chapoton and by J.-L. Loday and the third author, in order to describe operads related to the Stasheff polytopes. The vector space ST spanned by the faces of permutohedra has a natural structure of tridendriform bialgebra, we prove that it is free as a tridendriform algebra and exhibit a basis. Our result implies that the subspace of primitive elements of the coalgebra ST, equipped with the coboundary map of permutohedra, is a free cacti algebra. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free