Hopf algebras of rooted forests, cocyles, and free Rota-Baxter algebras

DOI10.1063/1.4963727zbMath1351.81076arXiv1605.09531OpenAlexW2410440865MaRDI QIDQ2832705

Tianjie Zhang, Li Guo, Xing Gao

Publication date: 14 November 2016

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.09531

Mathematics Subject Classification ID

Trees (05C05) (Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) (16E40) Connections of Hopf algebras with combinatorics (16T30) Yang-Baxter equations and Rota-Baxter operators (17B38)

Related Items (25)

Hopf algebra structure on free Rota-Baxter algebras by angularly decorated rooted trees ⋮ Hopf algebra of multidecorated rooted forests, free matching Rota-Baxter algebras and Gröbner-Shirshov bases ⋮ Dendriform-Nijenhuis bialgebras and DN-associative Yang-Baxter equations ⋮ Free Rota-Baxter systems and a Hopf algebra structure ⋮ Rota-Baxter paired modules and their constructions from Hopf algebras ⋮ Hopf algebras of planar binary trees: an operated algebra approach ⋮ Bimodules over relative Rota-Baxter algebras and cohomologies ⋮ Construction of free commutative Reynolds algebras by Gröbner-Shirshov bases ⋮ Rota-Baxter Leibniz algebras and their constructions ⋮ Locality and renormalization: Universal properties and integrals on trees ⋮ Left counital Hopf algebras on bi-decorated planar rooted forests and Rota-Baxter systems ⋮ λ-TD algebras, generalized shuffle products and left counital Hopf algebras ⋮ Unnamed Item ⋮ A Hopf algebra on subgraphs of a graph ⋮ Modified Rota-Baxter algebras, shuffle products and Hopf algebras ⋮ On weak peak quasisymmetric functions ⋮ Left counital Hopf algebras on free Nijenhuis algebras ⋮ Weighted infinitesimal unitary bialgebras of rooted forests, symmetric cocycles and pre-Lie algebras ⋮ Reynolds algebras and their free objects from bracketed words and rooted trees ⋮ Free Ω-Rota–Baxter algebras and Gröbner–Shirshov bases ⋮ Free nonunitary Rota-Baxter family algebras and typed leaf-spaced decorated planar rooted forests ⋮ Free Rota-Baxter family algebras and (tri)dendriform family algebras ⋮ Weighted infinitesimal unitary bialgebras on rooted forests and weighted cocycles ⋮ Free modified Rota-Baxter algebras and Hopf algebras ⋮ Infinitesimal unitary Hopf algebras and planar rooted forests

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