The hard Lefschetz theorem on Kähler Lie algebroids
Abstract
Compact Kähler manifolds classically satisfy the ard Lefschetz theorem, which gives strong control on the underlying topology of the manifold. One expects a similar theorem to be true for Kähler Lie algebroids, and we show for a certain class of them that this is indeed true, with an added ellipticity requirement. We provide examples of Lie algebroids satisfying this, as well as an example of a Kähler Lie algebroid that does not meet this ellipticity requirement and fails to satisfy the hard Lefschetz condition.
Fields of Study & Subjects
Homotopy and Cohomology in Algebraic Topology
Geometry and complex manifolds
Nonlinear Waves and Solitons
Publication details
- Journal / source
- Illinois Journal of Mathematics
- Publisher
- Duke University Press
- Volume
- 70
- Issue
- 1
- Pages
- 99-113
- Publication date
- 1 April 2026
- Language
- EN