Abstract
We calculate the test rank of a finite rank free metabelian Lie algebra over an arbitrary field and characterize the test sets for these algebras. We prove that each automorphism that is the identity modulo the derived subalgebra and that acts as the identity on some test set is an inner automorphism.
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References
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Chirkov, I.V., Shevelin, M.A. Test Sets in Free Metabelian Lie Algebras. Siberian Mathematical Journal 43, 1135–1140 (2002). https://doi.org/10.1023/A:1021185821646
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DOI: https://doi.org/10.1023/A:1021185821646