Hochschild cohomology parametrizes curved Morita deformations
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909523176849408 |
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| author | Lehmann, Alessandro |
| author_facet | Lehmann, Alessandro |
| contents | We show that, if one allows for curved deformations, the canonical map introduced in [KL09] between Morita deformations and second Hochschild cohomology of a dg algebra becomes a bijection. We also show that a bimodule induces an equivalence of curved deformations precisely when it induces an equivalence between the respective 1-derived categories. These results, together with arXiv:2402.08660, solve the curvature problem for first order deformations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_04945 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hochschild cohomology parametrizes curved Morita deformations Lehmann, Alessandro K-Theory and Homology 16E40 (Primary), 18G70 16E45, 18G80 (Secondary) We show that, if one allows for curved deformations, the canonical map introduced in [KL09] between Morita deformations and second Hochschild cohomology of a dg algebra becomes a bijection. We also show that a bimodule induces an equivalence of curved deformations precisely when it induces an equivalence between the respective 1-derived categories. These results, together with arXiv:2402.08660, solve the curvature problem for first order deformations. |
| title | Hochschild cohomology parametrizes curved Morita deformations |
| topic | K-Theory and Homology 16E40 (Primary), 18G70 16E45, 18G80 (Secondary) |
| url | https://arxiv.org/abs/2406.04945 |