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arXiv · 1408.0018

Lie algebroids generated by cohomology operators

D. García-Beltrán·J. A. Vallejo·Yu. Vorobiev
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Abstract

By studying the Fr\"olicher-Nijenhuis decomposition of cohomology operators (that is, derivations $D$ of the exterior algebra $\Omega (M)$ with $\mathbb{Z}-$degree $1$ and $D^2=0$), we describe new examples of Lie algebroid structures on the tangent bundle $TM$ (and its complexification $T^{\mathbb{C}}M$) constructed from pre-existing geometric ones such as foliations, complex, product or tangent structures. We also describe a class of Lie algebroids on tangent bundles associated to idempotent endomorphisms with nontrivial Nijenhuis torsion.

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D. García-Beltrán, J. A. Vallejo, Yu. Vorobiev. 2014-07-31. Lie algebroids generated by cohomology operators. https://doi.org/10.3934/jgm.2015.7.295

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