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Peer-reviewedCC BY 4.0Journal of Geometric Mechanics

Modular class of Lie ∞-algebroids and adjoint representations

  • Raquel Caseiro
  • Camille Laurent-Gengoux
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Abstract

We study the modular class of Q-manifolds, and in particular of negatively graded Lie ∞-algebroid. We show the equivalence of several descriptions of those classes, that it matches the classes introduced by various authors and that the notion is homotopy invariant. In the process, the adjoint and coadjoint actions up to homotopy of a Lie ∞-algebroid are spelled out. We also wrote down explicitly some dualities, e.g. between representations up to homotopies of Lie ∞-algebroids and their Q-manifold equivalent, which we hope to be of use for future reference.

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Cite

BibTeXRIS
BibTeX
@article{caseiro2026modular,
  title = {{Modular class of Lie $\infty$-algebroids and adjoint representations}},
  author = {Raquel Caseiro and Camille Laurent-Gengoux},
  journal = {Journal of Geometric Mechanics},
  year = {2026},
  month = sep,
  doi = {10.3934/jgm.2022008},
  eprint = {2203.16139},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-03632644v1},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Modular class of Lie ∞-algebroids and adjoint representations
AU  - Raquel Caseiro
AU  - Camille Laurent-Gengoux
PY  - 2026
DA  - 2026/09/03
JO  - Journal of Geometric Mechanics
DO  - 10.3934/jgm.2022008
UR  - https://hal.science/hal-03632644v1
AB  - We study the modular class of Q-manifolds, and in particular of negatively graded Lie ∞-algebroid. We show the equivalence of several descriptions of those classes, that it matches the classes introduced by various authors and that the notion is homotopy invariant. In the process, the adjoint and coadjoint actions up to homotopy of a Lie ∞-algebroid are spelled out. We also wrote down explicitly some dualities, e.g. between representations up to homotopies of Lie ∞-algebroids and their Q-manifold equivalent, which we hope to be of use for future reference.
SN  - 1941-4889
SN  - 1941-4897
ER  -