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arXiv · 2609.23527

Transferred $L_\infty$-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 $L_\infty$-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 $L_\infty$-formal, and contrast this with Wong's non-formality result for the dual numbers $\mathbb{K}[θ]/\langle θ^2 \rangle$, leading to a general formality classification problem.

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Zixu Li, Liyu Liu, Lingchao Meng. 2026-09-20. Transferred $L_\infty$-structures and a classification of binary brackets for finite-dimensional skew-gentle algebras. https://arxiv.org/abs/2609.23527

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