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Journal of Lie Theory 29 (2019), No. 3, 881--899
Copyright Heldermann Verlag 2019

Higher Omni-Lie Algebroids

Yanhui Bi
College Math. Inform. Science, Nanchang Hangkong University, Nanchang 330063, P. R. China

Luca Vitagliano
Dip. di Matematica, Univ. degli Studi di Salerno, 84084 Fisciano, Italy

Tao Zhang
College Math. Inform. Science, Henan Normal University, Xinxiang 453007, P. R. China

We propose a definition of a "higher" version of the omni-Lie algebroid and study its isotropic and involutive subbundles. Our higher omni-Lie algebroid is to (multi)contact and related geometries what the higher generalized tangent bundle of Zambon and Bi/Sheng is to (multi)symplectic and related geometries.

Keywords: Vector bundle form, higher omni-Lie algebroid, Dirac structure, generalized geometry.

MSC: 17B66, 53D18

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