$A_\infty$-deformations of zigzag algebras via Ginzburg dg algebras
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908336851517440 |
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| author | Liu, Junyang Wang, Zhengfang |
| author_facet | Liu, Junyang Wang, Zhengfang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_06757 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $A_\infty$-deformations of zigzag algebras via Ginzburg dg algebras Liu, Junyang Wang, Zhengfang Representation Theory Quantum Algebra Symplectic Geometry 16E05, 13D03, 16G20, 16E60 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. |
| title | $A_\infty$-deformations of zigzag algebras via Ginzburg dg algebras |
| topic | Representation Theory Quantum Algebra Symplectic Geometry 16E05, 13D03, 16G20, 16E60 |
| url | https://arxiv.org/abs/2301.06757 |