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PreprintCC BY 4.0arXiv

Deformation theory and the controlling L∞-structure of extended Rota-Baxter algebras

  • Jian Yang
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Abstract

In this paper, we introduce the controlling L∞[1]-algebra of extended Rota-Baxter algebras. As applications, we obtain the cohomology of extended Rota-Baxter algebras and homotopy extended Rota-Baxter algebras. We also study abelian extensions and formal deformations by the lower cohomology group. Lastly, we describe the intrinsic relationship among extended Rota-Baxter algebras, extended Rota-Baxter Lie algebras, and the eigenvalues of the extended Rota-Baxter operator. As the generalization of Rota-Baxter algebras with weight and modified Rota-Baxter algebras, the corresponding results also hold for those algebras.

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Cite

BibTeXRIS
BibTeX
@misc{yang2026deformation,
  title = {{Deformation theory and the controlling $L_\infty$-structure of extended Rota-Baxter algebras}},
  author = {Jian Yang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.01304},
  eprint = {2609.01304},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.01304},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Deformation theory and the controlling L_∞-structure of extended Rota-Baxter algebras
AU  - Jian Yang
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.01304
UR  - https://arxiv.org/abs/2609.01304
AB  - In this paper, we introduce the controlling L_∞[1]-algebra of extended Rota-Baxter algebras. As applications, we obtain the cohomology of extended Rota-Baxter algebras and homotopy extended Rota-Baxter algebras. We also study abelian extensions and formal deformations by the lower cohomology group. Lastly, we describe the intrinsic relationship among extended Rota-Baxter algebras, extended Rota-Baxter Lie algebras, and the eigenvalues of the extended Rota-Baxter operator. As the generalization of Rota-Baxter algebras with weight and modified Rota-Baxter algebras, the corresponding results also hold for those algebras.
ER  -