Representations and Modules of Rota-Baxter Algebras

Li Guo; Zongzhu Lin

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arXiv · 1905.01531

Representations and Modules of Rota-Baxter Algebras

Li Guo·Zongzhu Lin

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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.

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BibTeX RIS

Li Guo, Zongzhu Lin. 2019-05-04. Representations and Modules of Rota-Baxter Algebras. https://arxiv.org/abs/1905.01531

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