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arXiv · 2406.04945

Hochschild cohomology parametrizes curved Morita deformations

Alessandro Lehmann
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Abstract

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.

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Alessandro Lehmann. 2024-06-07. Hochschild cohomology parametrizes curved Morita deformations. https://doi.org/10.1090/proc%2F17133

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