Hopf algebra structures on free unitary extended Rota–Baxter algebras
Colloquium Mathematicum
MSC: Primary 16W99; Secondary 17B38
DOI: 10.4064/cm9795-2-2026
Published online: 15 September 2026
Abstract
As a common generalization of operator forms of the classical Yang–Baxter equation and the modified classical Yang–Baxter equation, an extended Rota–Baxter operator has been found in various algebraic structures, such as Laurent series, owing to their importance in the Hopf algebraic approach of Connes and Kreimer to renormalization in quantum field theory. We present an explicit construction of free objects in the category of extended Rota–Baxter algebras via bracketed words. We then equip this free object with a bialgebra structure via its universal property, and further show that the free object possesses a Hopf algebra structure.
