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Peer-reviewedCC BYSelecta Mathematica

Lie algebroids are curved Lie algebras

  • Damien Calaque1,2
  • Ricardo Campos3,2
  • Joost Nuiten3,2
  1. 1IMAG, Univ. Montpellier, CNRS, Montpellier, France
  2. 2Institut Montpelliérain Alexander Grothendieck
  3. 3Univ. Toulouse, INUC, UT2J, INSA Toulouse, TSE, CNRS, IMT, Toulouse, France
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Abstract

We show that there is an equivalence of ∞ ∞ -categories between Lie algebroids and certain kinds of curved Lie algebras. For this we develop a method to study the ∞ ∞ -category of curved Lie algebras using the homotopy theory of algebras over a complete operad.

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Cite

BibTeXRIS
BibTeX
@article{calaque2026algebroids,
  title = {{Lie algebroids are curved Lie algebras}},
  author = {Damien Calaque and Ricardo Campos and Joost Nuiten},
  journal = {Selecta Mathematica},
  year = {2026},
  month = jun,
  doi = {10.1007/s00029-026-01158-6},
  url = {https://doi.org/10.1007/s00029-026-01158-6},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Lie algebroids are curved Lie algebras
AU  - Damien Calaque
AU  - Ricardo Campos
AU  - Joost Nuiten
PY  - 2026
DA  - 2026/06/29
JO  - Selecta Mathematica
DO  - 10.1007/s00029-026-01158-6
UR  - https://doi.org/10.1007/s00029-026-01158-6
AB  - We show that there is an equivalence of ∞ ∞ -categories between Lie algebroids and certain kinds of curved Lie algebras. For this we develop a method to study the ∞ ∞ -category of curved Lie algebras using the homotopy theory of algebras over a complete operad.
SN  - 1022-1824
SN  - 1420-9020
ER  -