2021•arXiv (Cornell University)Open access

Hopf algebra structure on free Rota-Baxter algebras by angularly decorated rooted trees

Xigou Zhang, Anqi Xu, Li Guo

Abstract

By means of a new notion of subforests of an angularly decorated rooted forest, we give a combinatorial construction of a coproduct on the free Rota-Baxter algebra on angularly decorated rooted forests. We show that this coproduct equips the Rota-Baxter algebra with a bialgebra structure and further a Hopf algebra structure.

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Key concepts: Coproduct, Hopf algebra, Bialgebra, Quasitriangular Hopf algebra, Mathematics, Representation theory of Hopf algebras, Algebra over a field, Filtered algebra