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PreprintarXiv licencearXiv

The center is the formal internal automorphism group

  • Sonja Farr
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Abstract

We prove that the deformation functor associated to an algebra over a sufficiently nice Koszul operad can be lifted to an operadic formal moduli problem over the Koszul dual operad. We further show that this operadic formal moduli problem corresponds to the derived center of the algebra under the operadic Lurie-Pridham correspondence. As an application, we prove that the classical Gerstenhaber algebra structure on polyvector fields of a commutative algebra agrees with the derived center of the algebra as an abelian Poisson algebra.

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Cite

BibTeXRIS
BibTeX
@misc{farr2026center,
  title = {{The center is the formal internal automorphism group}},
  author = {Sonja Farr},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.31411},
  eprint = {2610.31411},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.31411},
}
RIS
TY  - UNPB
TI  - The center is the formal internal automorphism group
AU  - Sonja Farr
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2610.31411
UR  - https://arxiv.org/abs/2610.31411
AB  - We prove that the deformation functor associated to an algebra over a sufficiently nice Koszul operad can be lifted to an operadic formal moduli problem over the Koszul dual operad. We further show that this operadic formal moduli problem corresponds to the derived center of the algebra under the operadic Lurie-Pridham correspondence. As an application, we prove that the classical Gerstenhaber algebra structure on polyvector fields of a commutative algebra agrees with the derived center of the algebra as an abelian Poisson algebra.
ER  -