Derived equivalences of DG algebras are not governed by their cohomology rings
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915461081333760 |
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| author | Mao, X. -F. Lu, R. -K. |
| author_facet | Mao, X. -F. Lu, R. -K. |
| contents | Let $\mathscr{A}$ and $\mathscr{B}$ be two connected cochain DG algebra such that $\mathscr{A}^{\#}=\mathscr{B}^{\#}$ and the cohomology rings $H(\mathscr{A})$ and $H(\mathscr{B})$ are isomorphic. We give examples to show that $\mathscr{A}$ and $\mathscr{B}$ are not necessarily derived equivalent, thereby answering to a question of Dugas. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_17574 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Derived equivalences of DG algebras are not governed by their cohomology rings Mao, X. -F. Lu, R. -K. Rings and Algebras 16E45, 16E65, 16W20, 16W50 Let $\mathscr{A}$ and $\mathscr{B}$ be two connected cochain DG algebra such that $\mathscr{A}^{\#}=\mathscr{B}^{\#}$ and the cohomology rings $H(\mathscr{A})$ and $H(\mathscr{B})$ are isomorphic. We give examples to show that $\mathscr{A}$ and $\mathscr{B}$ are not necessarily derived equivalent, thereby answering to a question of Dugas. |
| title | Derived equivalences of DG algebras are not governed by their cohomology rings |
| topic | Rings and Algebras 16E45, 16E65, 16W20, 16W50 |
| url | https://arxiv.org/abs/2508.17574 |