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PreprintCC0arXiv

Transferred L∞-structures and a classification of binary brackets for finite-dimensional skew-gentle algebras

  • Zixu Li
  • Liyu Liu
  • Lingchao Meng
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Abstract

We construct a transferred L∞-structure on the shifted Chouhy--Solotar cochain complex of a finite-dimensional skew-gentle algebra and give explicit basis-level formulas for its binary operation l2 in all shifted degrees. We further prove that the Hochschild dg Lie algebra of an An-type skew-gentle algebra is homotopy abelian, and hence L∞-formal, and contrast this with Wong's non-formality result for the dual numbers 𝕂[θ]/⟨ θ2 ⟩, leading to a general formality classification problem.

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Cite

BibTeXRIS
BibTeX
@misc{li2026transferred,
  title = {{Transferred $L_\infty$-structures and a classification of binary brackets for finite-dimensional skew-gentle algebras}},
  author = {Zixu Li and Liyu Liu and Lingchao Meng},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.23527},
  eprint = {2609.23527},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.23527},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - Transferred L_∞-structures and a classification of binary brackets for finite-dimensional skew-gentle algebras
AU  - Zixu Li
AU  - Liyu Liu
AU  - Lingchao Meng
PY  - 2026
DA  - 2026/09/20
PB  - arXiv
DO  - 10.48550/arxiv.2609.23527
UR  - https://arxiv.org/abs/2609.23527
AB  - We construct a transferred L_∞-structure on the shifted Chouhy--Solotar cochain complex of a finite-dimensional skew-gentle algebra and give explicit basis-level formulas for its binary operation l_2 in all shifted degrees. We further prove that the Hochschild dg Lie algebra of an A_n-type skew-gentle algebra is homotopy abelian, and hence L_∞-formal, and contrast this with Wong's non-formality result for the dual numbers 𝕂[θ]/⟨ θ^2 ⟩, leading to a general formality classification problem.
ER  -