Lie algebroids generated by cohomology operators

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

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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 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 languageEnglish
Pages (from-to)295-315
Number of pages21
JournalJournal of Geometric Mechanics
Volume7
Issue number3
DOIs
StatePublished - 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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