Representations and modules of Rota–Baxter algebras

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.

Keywords

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

2010 Mathematics Subject Classification

16D90, 16G99, 16S32, 16W99

The full text of this article is unavailable through your IP address: 172.17.0.1

Received 3 January 2020

Accepted 16 July 2021

Published 24 October 2022