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arXiv · 2301.06757

$A_\infty$-deformations of zigzag algebras via Ginzburg dg algebras

Junyang Liu·Zhengfang Wang
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Abstract

This note aims to give a short proof of the recent result due to Etg\"u-Lekili (2017) and Lekili-Ueda (2021): the zigzag algebra of any finite tree over a field of characteristic 0 is intrinsically formal if and only if the tree is of type ADE. We also complete the proof of this result by considering a field of arbitrary characteristic for type E, which was still open.

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BibTeXRIS

Junyang Liu, Zhengfang Wang. 2023-01-17. $A_\infty$-deformations of zigzag algebras via Ginzburg dg algebras. https://doi.org/10.1016/j.jalgebra.2025.03.057

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