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Algorithm to compute the maximal abelian dimension of Lie algebras

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Abstract

In this paper, the maximal abelian dimension is computationally obtained for an arbitrary finite-dimensional Lie algebra, defined by its nonzero brackets. More concretely, we describe and implement an algorithm which computes such a dimension by running it in the symbolic computation package MAPLE. Finally, we also show a computational study related to this implementation, regarding both the computing time and the memory used.

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Authors and Affiliations

  1. Dpto. Geometría y Topología, Universidad de Sevilla, Seville, Spain

    M. Ceballos & J. Núñez

  2. Dpto. Economía, Mét. Cuant. e H. Ec., Universidad Pablo de Olavide, Seville, Spain

    A. F. Tenorio

Authors
  1. M. Ceballos
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  2. J. Núñez
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  3. A. F. Tenorio
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Corresponding author

Correspondence to A. F. Tenorio.

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Ceballos, M., Núñez, J. & Tenorio, A.F. Algorithm to compute the maximal abelian dimension of Lie algebras. Computing 84, 231–239 (2009). https://doi.org/10.1007/s00607-009-0029-8

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  • DOI: https://doi.org/10.1007/s00607-009-0029-8

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