Transferred $L_\infty$-structures and a classification of binary brackets for finite-dimensional skew-gentle algebras
Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Li, Zixu, Liu, Liyu, Meng, Lingchao
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214054352