FREE ROTA–BAXTER ALGEBRAS AND ROOTED TREES

• DOI: 10.1142/s0219498808002746
• Publication Date: 2008-04-28T11:04:25Z
• Authors: KURUSCH EBRAHIMI-...; LI GUO
• Keywords: Noncommutative algebraic geometry; Operator algebra

A Rota–Baxter algebra, also known as a Baxter is an algebra with linear operator satisfying relation, called the that generalizes integration by parts formula. Most of studies on algebras have been for commutative algebras. Two constructions free were obtained Rota and Cartier in 1970s third one Keigher authors 1990s terms mixable shuffles. Recently, noncommutative appeared both physics connection work Connes Kreimer renormalization perturbative quantum field theory, mathematics related to Loday Ronco dendriform dialgebras trialgebras. This paper uses rooted trees forests give explicit modules sets. highlights combinatorial nature facilitates their further study. As application, we obtain unitarization