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On Some Properties of Lie-Centroids of Leibniz Algebras

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Abstract

We study some properties of \(\mathsf {Lie}\)-centroids related to central \(\mathsf {Lie}\)-derivations, generalized \(\mathsf {Lie}\)-derivations and almost inner \(\mathsf {Lie}\)-derivations. We also determine the \(\mathsf {Lie}\)-centroid of the tensor product of a commutative associative algebra and a Leibniz algebra.

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Acknowledgements

We would like to thank the anonymous referees for their helpful comments and remarks that greatly improved the quality of the paper. The first and second authors were supported by Ministerio de Ciencia e Innovación (Spain), with grant number PID2020-115155GB-I00. The second author is a Postdoctoral Fellow of the Research Foundation–Flanders (FWO).

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Author notes

  1. Xabier García-Martínez and Natalia Pacheco-Rego have contributed equally to this work.

Authors and Affiliations

  1. Departamento de Matemática Aplicada I and CITMaga, Universidade de Vigo, E. E. Forestal, 36005 , Campus de Pontevedra, Pontevedra, Spain

    José Manuel Casas Mirás

  2. Departamento de Matemáticas and CITMaga, Universidade de Vigo, Esc. Sup. de Enx. Informática, Campus de Ourense, 32004, Ourense, Spain

    Xabier García-Martínez

  3. Faculty of Engineering, Vrije Universiteit Brussel, Pleinlaan 2, 1050, Brussel, Belgium

    Xabier García-Martínez

  4. Polytechnical Institute of Cavado and Ave, Campus do IPCA, 4750-810, Vila Frescainha, S. Martinho, Barcelos, Portugal

    Natalia Pacheco-Rego

Authors
  1. José Manuel Casas Mirás
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  2. Xabier García-Martínez
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  3. Natalia Pacheco-Rego
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Correspondence to José Manuel Casas Mirás.

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Communicated by Rosihan M. Ali.

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Mirás, J.M.C., García-Martínez, X. & Pacheco-Rego, N. On Some Properties of Lie-Centroids of Leibniz Algebras. Bull. Malays. Math. Sci. Soc. 45, 3499–3520 (2022). https://doi.org/10.1007/s40840-022-01389-8

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