Lie algebroids generated by cohomology operators

Abstract

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.

Second version

References in corpus (5)

• Lectures on Integrability of Lie Brackets
• Lie Algebroids in Classical Mechanics and Optimal Control
• Brackets
• Courant-Nijenhuis tensors and generalized geometries
• Deformations of Lie brackets: cohomological aspects

Cited by in corpus (1)

• Infinitesimal Poisson Algebras and Linearization of Hamiltonian Systems