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Relations Between Combinatorial Structures and Lie Algebras: Centers and Derived Lie Algebras

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Abstract

In this paper, we study how two important ideals of a given Lie algebra \(\mathfrak {g}\) (namely, the center \(Z(\mathfrak {g})\) and the derived Lie algebra \(\mathcal {D}(\mathfrak {g})\)) can be translated into the language of Graph Theory. In this way, we obtain some criteria and characterizations of these ideals using Graph Theory.

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Acknowledgments

This work has been partially supported by MTM2010-19336 and FEDER. Additionally, the authors want to thank the referees for their helpful and useful comments and suggestions, which have allowed us to improve the quality of this paper.

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Authors and Affiliations

  1. Departamento de Geometría y Topología, Facultad de Matemáticas, Universidad de Sevilla, Aptdo. 1160, Seville, 41080, Spain

    Manuel Ceballos & Juan Núñez

  2. Dpto. de Economía, Métodos Cuantitativos e H.a Económica, Escuela Politécnica Superior, Universidad Pablo de Olavide, Ctra. Utrera km. 1, Seville, 41013, Spain

    Ángel F. Tenorio

Authors
  1. Manuel Ceballos
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  2. Juan Núñez
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  3. Ángel F. Tenorio
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Correspondence to Manuel Ceballos.

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Communicated by Ang Miin Huey.

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Ceballos, M., Núñez, J. & Tenorio, Á.F. Relations Between Combinatorial Structures and Lie Algebras: Centers and Derived Lie Algebras. Bull. Malays. Math. Sci. Soc. 38, 529–541 (2015). https://doi.org/10.1007/s40840-014-0034-8

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  • DOI: https://doi.org/10.1007/s40840-014-0034-8

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