Article Dans Une Revue J.Geom.Mech. Année : 2022

Modular class of Lie $\infty$-algebroids and adjoint representation

Résumé

We study the modular class of $Q$-manifolds, and in particular of negatively graded Lie $\infty$-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 $\infty$-algebroid are spelled out. We also wrote down explicitly some dualities, e.g. between representations up to homotopies of Lie $\infty$-algebroids and their $Q$-manifold equivalent, which we hope to be of use for future reference.

Dates et versions

hal-03632644 , version 1 (06-04-2022)

Identifiants

Citer

Raquel Caseiro, Camille Laurent-Gengoux. Modular class of Lie $\infty$-algebroids and adjoint representation. J.Geom.Mech., 2022, 14 (2), pp.273-305. ⟨10.3934/jgm.2022008⟩. ⟨hal-03632644⟩
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