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arXiv · 2503.05317

Derived derivations govern contraderived deformations of dg algebras over dg (pr)operads

J. P. Pridham
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Abstract

We show that Hinich's simplicial nerve of the differential graded Lie algebra (DGLA) of derived derivations of a dg algebra $A$ over a dg properad $\mathcal{P}$ is equivalent to the space of deformations of $A$ as a $\mathcal{P}_{\infty}$-algebra in Positselski's contraderived dg category. This resolves Hinich's counterexamples to the general existence of derived deformations. It also generalises his results when $A$ is homologically bounded below, since contraderived deformations are then precisely derived deformations.

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J. P. Pridham. 2025-03-07. Derived derivations govern contraderived deformations of dg algebras over dg (pr)operads. https://arxiv.org/abs/2503.05317

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