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Quotients in Graded Lie Algebras. Martindale-like Quotients for Kantor Pairs and Lie Triple Systems

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Abstract

In this paper we prove that the maximal algebra of quotients of a nondegenerate Lie algebra with a short ℤ-grading is ℤ-graded with the same support. As a consequence, we introduce a notion of Martindale-like quotients for Kantor pairs and Lie triple systems and construct their maximal systems of quotients.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, Universidad Rey Juan Carlos, 28933, Móstoles (Madrid), Spain

    Esther García

  2. Departamento de Álgebra, Geometría y Topología, Universidad de Málaga, 29071, Málaga, Spain

    Miguel Gómez Lozano

Authors
  1. Esther García
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  2. Miguel Gómez Lozano
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Corresponding author

Correspondence to Esther García.

Additional information

Presented by Alain Verschoren.

The first author was partially supported by the MEC and Fondos FEDER MTM2010-16153, by FMQ 264, and by MICINN I3-2010/00075/001.

The second author was partially supported by the MEC and Fondos FEDER MTM2010-19482, by FMQ 264 and FQM 3737, and by MICINN I3-2010/00075/001.

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García, E., Gómez Lozano, M. Quotients in Graded Lie Algebras. Martindale-like Quotients for Kantor Pairs and Lie Triple Systems. Algebr Represent Theor 16, 229–238 (2013). https://doi.org/10.1007/s10468-011-9303-5

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  • DOI: https://doi.org/10.1007/s10468-011-9303-5

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