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Lie algebroids generated by cohomology operators

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  • By studying the Frölicher-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.
    Mathematics Subject Classification: Primary: 58J10, 53D17; Secondary: 20G10.


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