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.
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We would like to thank Shiraz University for supporting this paper by grant no. 92grd1m82582 of Shiraz University, Iran.
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Armakan, A.R., Farhangdoost, M.R. Extensions of hom-Lie algebras in terms of cohomology. Czech Math J 67, 317–328 (2017). https://doi.org/10.21136/CMJ.2017.0576-15
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DOI: https://doi.org/10.21136/CMJ.2017.0576-15