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 Ω(M) with ℤ-degree 1 and D2 = 0), we describe new examples of Lie algebroid structures on the tangent bundle TM (and its complexification Tℂ 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 idem-potent endomorphisms with nontrivial Nijenhuis torsion. © American Institute of Mathematical Sciences.
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Cohomology operators; Complex structures; Lie algebroids; Product structures; Sprays; Tangent structures
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