Representations and Modules of Rota-Baxter Algebras

Abstract

We give a broad 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 an 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 is also formulated.

28 pages

References in corpus (3)

• Combinatorics of renormalization as matrix calculus
• Rota-Baxter Categories
• Braided Rota-Baxter algebras, quantum quasi-shuffle algebras and braided dendriform algebras

Cited by in corpus (5)

• Representations and cohomologies of relative Rota-Baxter Lie algebras and applications
• Spectrum of Rota-Baxter operators
• An example of a simple double Lie algebra
• Modules of polynomial Rota-Baxter Algebras and matrix equations
• Rota-Baxter $C^{\ast }$-algebras