Hochschild cohomology parametrizes curved Morita deformations
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- by Alessandro Lehmann;
- Proc. Amer. Math. Soc. 153 (2025), 2341-2351
- DOI: https://doi.org/10.1090/proc/17133
- Published electronically: March 25, 2025
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Abstract:
We show that, if one allows for curved deformations, the canonical map introduced by Keller and Lowen [Int. Math. Res. Not. IMRN 17 (2009), 3221–3235] 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 the results of Lehmann and Lowen [Filtered derived categories of curved deformations, https://arxiv.org/abs/2402.08660, 2024], offer a solution to the curvature problem for first order deformations.References
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Bibliographic Information
- Alessandro Lehmann
- Affiliation: Departement Wiskunde, Universiteit Antwerpen, Middelheimcampus, Middelheimlaan 1, 2020 Antwerp, Belgium; \normalfont{and} SISSA, Via Bonomea 265, 34136 Trieste TS, Italy
- ORCID: 0009-0006-1511-8265
- Email: alessandro.lehmann@uantwerpen.be, alehmann@sissa.it
- Received by editor(s): June 14, 2024
- Received by editor(s) in revised form: October 24, 2024, and October 28, 2024
- Published electronically: March 25, 2025
- Additional Notes: This project received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 817762).
- Communicated by: Sarah Witherspoon
- © Copyright 2025 by Alessandro Lehmann
- Journal: Proc. Amer. Math. Soc. 153 (2025), 2341-2351
- MSC (2020): Primary 16E40; Secondary 18G70, 16E45, 18G80
- DOI: https://doi.org/10.1090/proc/17133
- MathSciNet review: 4892611