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

Junyang Liu; Zhengfang Wang

doi:10.1016/j.jalgebra.2025.03.057

paper

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

arXiv:2301.06757 · doi:10.1016/j.jalgebra.2025.03.057

Abstract

This note aims to give a short proof of the recent result due to Etgü-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.

7 pages; v2: many minor changes; v3: minor changes, appeared in Journal of Algebra

A∞​-deformations of zigzag algebras via Ginzburg dg algebras

Abstract

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