Mathematics > Algebraic Geometry
[Submitted on 7 Mar 2025
]
Title: Derived derivations govern contraderived deformations of dg algebras over dg (pr)operads
Title: 导出导数支配dg代数关于dg (pr)operads的反导数变形
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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