`a`
The Journal of Geometric Mechanics (JGM)
 

Lie algebroids generated by cohomology operators

Pages: 295 - 315, Volume 7, Issue 3, September 2015      doi:10.3934/jgm.2015.7.295

 
       Abstract        References        Full Text (458.3K)       Related Articles       

Dennise García-Beltrán - Departamento de Matemáticas, Universidad de Sonora, Blvd. Encinas y Rosales, Edi cio 3K-1, Hermosillo, Son 83000, Mexico (email)
José A. Vallejo - Facultad de Ciencias, Universidad Autónoma de San Luis Potosí, Lat. Av. Salvador Nava s/n Col. Lomas, San Luis Potosí, SLP 78290, Mexico (email)
Yurii Vorobiev - Departamento de Matemáticas, Universidad de Sonora, Blvd. Encinas y Rosales, Edificio 3K-1, Hermosillo, Son 83000, Mexico (email)

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.

Keywords:  Lie algebroids, cohomology operators, product structures, complex structures, tangent structures, sprays.
Mathematics Subject Classification:  Primary: 58J10, 53D17; Secondary: 20G10.

Received: October 2014;      Revised: May 2015;      Available Online: July 2015.

 References