Czechoslovak Mathematical Journal

, Volume 67, Issue 2, pp 317–328

Extensions of hom-Lie algebras in terms of cohomology

  • Abdoreza R. Armakan
  • Mohammed Reza Farhangdoost
Article

Abstract

We study (non-abelian) extensions of a given hom-Lie algebra and provide a geometrical interpretation of extensions, in particular, we characterize an extension of a hom-Lie algebra g by another hom-Lie algebra h and discuss the case where h has no center. We also deal with the setting of covariant exterior derivatives, Chevalley derivative, Maurer-Cartan formula, curvature and the Bianchi identity for the possible extensions in differential geometry. Moreover, we find a cohomological obstruction to the existence of extensions of hom-Lie algebras, i.e., we show that in order to have an extendible hom-Lie algebra, there should exist a trivial member of the third cohomology.

Keywords

hom-Lie algebras cohomology of hom-Lie algebras extensions of hom-Lie algebras 

MSC 2010

17B99 55U15 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2017

Authors and Affiliations

  • Abdoreza R. Armakan
    • 1
  • Mohammed Reza Farhangdoost
    • 1
  1. 1.Department of Mathematics, College of SciencesShiraz university, Adabiat squareShiraz, FarsIran

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