Abstract
A relative Rota-Baxter algebra is a generalization of a Rota-Baxter algebra. Relative Rota-Baxter algebras are closely related to dendriform algebras. In this paper, we introduce bimodules over a relative Rota-Baxter algebra that fits with the representations of dendriform algebras. We define the cohomology of a relative Rota-Baxter algebra with coefficients in a bimodule and then study abelian extenfsions of relative Rota-Baxter algebras in terms of the second cohomology group. Finally, we consider homotopy relative Rota-Baxter algebras and classify skeletal homotopy relative Rota-Baxter algebras in terms of the above-defined cohomology.
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Acknowledgements
We thank the anonymous referee for his useful comments and suggestions, which improved the presentation of the article. A. Das would like to thank IIT Kharagpur (India) for providing a beautiful academic atmosphere where some parts of the research were carried out. Some part of the research work of S. K. Mishra was supported by the NBHM postdoctoral fellowship, India.
Funding
The research work of S. K. Mishra was supported by NBHM Postdoctoral Fellowship (Grant number 0204/8/2020/R&D-II/9976).
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Das, A., Mishra, S.K. Bimodules over Relative Rota-Baxter Algebras and Cohomologies. Algebr Represent Theor 26, 1823–1848 (2023). https://doi.org/10.1007/s10468-022-10161-2
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DOI: https://doi.org/10.1007/s10468-022-10161-2