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

Tianjie Zhang, Xing Gao, Li Guo

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


The Hopf algebra and the Rota-Baxter algebra are the two algebraic structures underlying the algebraic approach of Connes and Kreimer to renormalization of perturbative quantum field theory. In particular, the Hopf algebra of rooted trees serves as the "baby model" of Feynman graphs in their approach and can be characterized by certain universal properties involving a Hochschild 1-cocycle. Decorated rooted trees have also been applied to study Feynman graphs. We will continue the study of universal properties of various spaces of decorated rooted trees with such a 1-cocycle, leading to the concept of a cocycle Hopf algebra. We further apply the universal properties to equip a free Rota-Baxter algebra with the structure of a cocycle Hopf algebra.

Original languageEnglish (US)
Article number101701
JournalJournal of Mathematical Physics
Issue number10
StatePublished - Oct 1 2016

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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