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On the Capability of Hom-Lie Algebras

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Abstract

A Hom-Lie algebra \((L, \alpha _L)\) is said to be capable if there exists a Hom-Lie algebra \((H, \alpha _H)\) such that \(L \cong H/Z(H)\). We obtain a characterisation of capable Hom-Lie algebras involving its epicentre and we use this theory to further study the six-term exact sequence in homology and to obtain a Hopf-type formulae of the second homology of perfect Hom-Lie algebras.

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Acknowledgements

The authors would like to thank the referee for his helpful comments and suggestions that improved the manuscript.

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Authors and Affiliations

  1. Dpto. Matemática Aplicada I, CITMaga and Universidade de Vigo, 15782/36005, Santiago de Compostela/Pontevedra, Spain

    José Manuel Casas

  2. Departamento de Matemáticas, CITMaga and Universidade de Vigo, 15782/32004, Santiago de Compostela/Ourense, Spain

    Xabier García-Martínez

  3. Faculty of Engineering, Vrije Universiteit Brussel, 1050, Brussels, Belgium

    Xabier García-Martínez

Authors
  1. José Manuel Casas
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  2. Xabier García-Martínez
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Correspondence to Xabier García-Martínez.

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This work was supported by Ministerio de Economía y Competitividad (Spain), with grant number PID2020-115155GB-I00. X. García-Martínez is a Postdoctoral Fellow of the Research Foundation–Flanders (FWO).

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Casas, J.M., García-Martínez, X. On the Capability of Hom-Lie Algebras. Mediterr. J. Math. 19, 86 (2022). https://doi.org/10.1007/s00009-021-01937-9

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  • DOI: https://doi.org/10.1007/s00009-021-01937-9

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