Lie algebroids generated by cohomology operators

Dennise  García-Beltrán; José A.  Vallejo; Yurii  Vorobiev

doi:10.3934/jgm.2015.7.295

Article Contents

2015, Volume 7, Issue 3: 295-315. Doi: 10.3934/jgm.2015.7.295

This issue Previous Article Two-component higher order Camassa-Holm systems with fractional inertia operator: A geometric approach Next Article Models for higher algebroids

Lie algebroids generated by cohomology operators

1.
Departamento de Matemáticas, Universidad de Sonora, Blvd. Encinas y Rosales, Edicio 3K-1, Hermosillo, Son 83000
2.
Facultad de Ciencias, Universidad Autónoma de San Luis Potosí, Lat. Av. Salvador Nava s/n Col. Lomas, San Luis Potosí, SLP 78290
3.
Departamento de Matemáticas, Universidad de Sonora, Blvd. Encinas y Rosales, Edificio 3K-1, Hermosillo, Son 83000

Received: October 2014

Revised: May 2015

Published: September 2015

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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.

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Mathematics Subject Classification: Primary: 58J10, 53D17; Secondary: 20G10.

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