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Computing Levi Decompositions in Lie algebras

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Abstract.

 We consider the algorithmic problem of computing Levi decompositions in Lie algebras and Wedderburn–Malcev decompositions in associative algebras over the field of rational numbers. We propose deterministic polynomial time algorithms for both problems. The methods are based on the corresponding classical existence theorems. Computational experiences are discussed at the end of the paper.

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Authors and Affiliations

  1. Department of Mathematics and Computing Science, Technical University of Eindhoven, P.O. Box 513, NL-5600 MB Eindhoven, The Netherlands (e-mail: wdg@win.tue.nl), , , , , , NL

    W. A. de Graaf

  2. Computer and Automation Institute, Hungarian Academy of Sciences, 1111 Budapest, Lágymányosi u. 11, Hungary (e-mail: ig@ilab.sztaki.hu), , , , , , HU

    G. Ivanyos

  3. Department of Mathematics and Computing Sciences, Faculty of Electrical Engineering and Informatics, Technical University of Budapest, Budapest, Hungary (e-mail: alex@vma.bme.hu), , , , , , HU

    A. Küronya

  4. Computer and Automation Institute, Hungarian, Academy of Sciences, 1111 Budapest, Lágymányosi u. 11, Hungary (e-mail: lajos@nyest.ilab.sztaki.hu), , , , , , HU

    L. Rónyai

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  1. W. A. de Graaf
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  2. G. Ivanyos
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  3. A. Küronya
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  4. L. Rónyai
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Received: October 24, 1995; revised version: May 28, 1996

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de Graaf, W., Ivanyos, G., Küronya, A. et al. Computing Levi Decompositions in Lie algebras. AAECC 8, 291–303 (1997). https://doi.org/10.1007/s002000050066

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  • DOI: https://doi.org/10.1007/s002000050066