Asian Journal of Mathematics

Volume 25 (2021)

Number 6

Representations and modules of Rota–Baxter algebras

Pages: 841 – 870



Li Guo (Department of Mathematics and Computer Science, Rutgers University, Newark, New Jersey, U.S.A.)

Zongzhu Lin (Department of Mathematics, Kansas State University, Manhattan, Ks., U.S.A.)


We give a general study of representation and module theory of Rota–Baxter algebras. Regular-singular decompositions of Rota–Baxter algebras and Rota–Baxter modules are obtained under the condition of quasi-idempotency. Representations of a Rota–Baxter algebra are shown to be equivalent to the representations of the ring of Rota–Baxter operators whose categorical properties are obtained and explicit constructions are provided. Representations from coalgebras are investigated and their algebraic Birkhoff factorization is given. Representations of Rota–Baxter algebras in the tensor category context are also formulated.


Rota–Baxter algebra, Rota–Baxter module, ring of Rota–Baxter operators, matrix representation, coalgebra

2010 Mathematics Subject Classification

16D90, 16G99, 16S32, 16W99

Received 3 January 2020

Accepted 16 July 2021

Published 24 October 2022