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Constructions of $3$-Lie algebroids
[Submitted on 23 Jun 2026] · 2026-06-25 · via math updates on arXiv.org

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Abstract:The paper investigates the construction of Lie algebroids and $3$-Lie algebroids via connections generated by finite families of differential operators and dual sections. We first recall the description of Lie and $n$-Lie algebroid brackets in terms of connections, and introduce an $n$-curvature operator whose $n$-Bianchi identity characterizes the fundamental identity. We then provide sufficient conditions under which such generating families determine Lie algebroid and $3$-Lie algebroid structures. The construction extends the single-operator approach and covers natural examples such as the Jacobi Lie algebroid. As an application, we construct a concrete $3$-Lie algebroid structure arising from Poisson Lie algebroid data.

Submission history

From: Begüm Ateşli [view email]
[v1] Tue, 23 Jun 2026 20:11:36 UTC (19 KB)

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