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Sibirskii Matematicheskii Zhurnal, 2004, Volume 45, Number 6, Pages 1391–1396 (Mi smj1148)  
This article is cited in 1 scientific paper (total in 1 paper)

Endomorphisms of free metabelian Lie algebras which preserve orbits

I. V. Chirkov, M. A. Shevelin

Omsk State University
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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.
Keywords: free metabelian Lie algebra, primitive elements, automorphism group, endomorphism, automorphic orbit of an element.
Received: 23.01.2004
English version:
Siberian Mathematical Journal, 2004, Volume 45, Issue 6, Pages 1135–1139
DOI: https://doi.org/10.1023/B:SIMJ.0000048929.00950.1f
Bibliographic databases:
UDC: 512.55
Language: Russian
Citation: I. V. Chirkov, M. A. Shevelin, “Endomorphisms of free metabelian Lie algebras which preserve orbits”, Sibirsk. Mat. Zh., 45:6 (2004), 1391–1396; Siberian Math. J., 45:6 (2004), 1135–1139
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
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