Derived derivations govern contraderived deformations of dg algebras over dg (pr)operads
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916646352846848 |
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| author | Pridham, J. P. |
| author_facet | Pridham, J. P. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_05317 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Derived derivations govern contraderived deformations of dg algebras over dg (pr)operads Pridham, J. P. Algebraic Geometry Quantum Algebra 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. |
| title | Derived derivations govern contraderived deformations of dg algebras over dg (pr)operads |
| topic | Algebraic Geometry Quantum Algebra |
| url | https://arxiv.org/abs/2503.05317 |