2013/04/03 by Kurusch Ebrahimi‐Fard, Ebrahimi-Fard, Kurusch, Frédéric Patras +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1304.1204
openalex publication_date 2013/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Gian-Carlo Rota suggested in one of his last articles the problem of developing a theory around the notion of integration algebras, complementary to the already existing theory of differential algebras. This idea was mainly motivated by Rota's deep appreciation for Kuo-Tsai Chen's seminal work on iterated integrals. As a starting point for such a theory of integration algebras Rota proposed to consider a particular operator identity first introduced by the mathematician Glen Baxter. Later it was coined Rota-Baxter identity. In this article we briefly recall basic properties of Rota--Baxter algebras, and present a concise review of recent work with a particular emphasis of noncommutative aspects.