Lie algebroids generated by cohomology operators

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

doi:10.3934/jgm.2015.7.295

Lie algebroids generated by cohomology operators

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

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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 T^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 idem-potent endomorphisms with nontrivial Nijenhuis torsion.

Original language	English
Pages (from-to)	295-315
Number of pages	21
Journal	Journal of Geometric Mechanics
Volume	7
Issue number	3
DOIs	https://doi.org/10.3934/jgm.2015.7.295
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

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10.3934/jgm.2015.7.295

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author = "Dennise Garc{\'i}a-Beltr{\'a}n and Vallejo, {Jos{\'e} A.} and Yurii Vorobiev",

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T1 - Lie algebroids generated by cohomology operators

AU - García-Beltrán, Dennise

AU - Vallejo, José A.

AU - Vorobiev, Yurii

N1 - Publisher Copyright: © American Institute of Mathematical Sciences.

PY - 2015/9/1

Y1 - 2015/9/1

N2 - 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.

AB - 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.

KW - Cohomology operators

KW - Complex structures

KW - Lie algebroids

KW - Product structures

KW - Sprays

KW - Tangent structures

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DO - 10.3934/jgm.2015.7.295

M3 - Artículo

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VL - 7

SP - 295

EP - 315

JO - Journal of Geometric Mechanics

JF - Journal of Geometric Mechanics

IS - 3

ER -

Lie algebroids generated by cohomology operators

Abstract

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Keywords

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