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arXiv · 2504.12550

The Hard Lefschetz Theorem on Kähler Lie Algebroids

Shane Rankin
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Abstract

Compact Kähler manifolds classically satisfy the Hard 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 consequently fails to satisfy the Hard Lefschetz condition.

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Shane Rankin. 2026-05-23. The Hard Lefschetz Theorem on Kähler Lie Algebroids. https://arxiv.org/abs/2504.12550

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