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PreprintCC BY 4.0arXiv

Deformations and the controlling L∞-structure of extended Rota-Baxter Lie algebras

  • Jian Yang
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Abstract

In this paper, we introduce the controlling L∞[1]-algebra of extended Rota-Baxter Lie algebras. As applications, we obtain the cohomology of extended Rota-Baxter Lie algebras. We also study abelian extensions and formal deformations by the lower cohomology group. Lastly, we get the notion of homotopy extended Rota-Baxter Lie algebras. Specifically, we present the controlling L∞[1]-algebra of modified Rota-Baxter Lie algebras and of Rota-Baxter Lie algebras with weight.

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Cite

BibTeXRIS
BibTeX
@misc{yang2026deformations,
  title = {{Deformations and the controlling $L_\infty$-structure of extended Rota-Baxter Lie algebras}},
  author = {Jian Yang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.29829},
  eprint = {2608.29829},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.29829},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Deformations and the controlling L_∞-structure of extended Rota-Baxter Lie algebras
AU  - Jian Yang
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2608.29829
UR  - https://arxiv.org/abs/2608.29829
AB  - In this paper, we introduce the controlling L_∞[1]-algebra of extended Rota-Baxter Lie algebras. As applications, we obtain the cohomology of extended Rota-Baxter Lie algebras. We also study abelian extensions and formal deformations by the lower cohomology group. Lastly, we get the notion of homotopy extended Rota-Baxter Lie algebras. Specifically, we present the controlling L_∞[1]-algebra of modified Rota-Baxter Lie algebras and of Rota-Baxter Lie algebras with weight.
ER  -