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Endomorphisms of Free Metabelian Lie Algebras Which Preserve Orbits

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Abstract

For the free rank 2 metabelian Lie algebra over an infinite field we prove that an endomorphism of the algebra which preserves the automorphic orbit of a nonzero element is an automorphism. We construct some counterexamples over finite fields.

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Authors and Affiliations

  1. Omsk State University, USA

    I. V. Chirkov & M. A. Shevelin

Authors
  1. I. V. Chirkov
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  2. M. A. Shevelin
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Chirkov, I.V., Shevelin, M.A. Endomorphisms of Free Metabelian Lie Algebras Which Preserve Orbits. Siberian Mathematical Journal 45, 1135–1139 (2004). https://doi.org/10.1023/B:SIMJ.0000048929.00950.1f

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  • DOI: https://doi.org/10.1023/B:SIMJ.0000048929.00950.1f

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