Abstract
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.
Original language | English |
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Pages (from-to) | 295-315 |
Number of pages | 21 |
Journal | Journal of Geometric Mechanics |
Volume | 7 |
Issue number | 3 |
DOIs | |
State | Published - 1 Sep 2015 |
Bibliographical note
Publisher Copyright:© American Institute of Mathematical Sciences.
Keywords
- Cohomology operators
- Complex structures
- Lie algebroids
- Product structures
- Sprays
- Tangent structures