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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Minimal nonnilpotent solvable Lie algebras


Author: Ernest L. Stitzinger
Journal: Proc. Amer. Math. Soc. 28 (1971), 47-49
MSC: Primary 17.30
DOI: https://doi.org/10.1090/S0002-9939-1971-0271178-X
MathSciNet review: 0271178
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Abstract: We shall say that a solvable Lie algebra $ L$ is a minimal nonnilpotent Lie algebra if $ L$ is nonnilpotent but all proper subalgebras of $ L$ are nilpotent. It is shown here that if $ L$ is a minimal nonnilpotent Lie algebra, then $ L$ is the vector space direct sum of $ A$ and $ F$ where $ A$ is an ideal in $ L,F$ is a one-dimensional subalgebra of $ L$, either $ A$ is a minimal ideal of $ L$ or the center of $ A$ coincides with the derived algebra, $ A'$, of $ A$ and in either case $ F$ acts irreducibly on $ A/A'$.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0271178-X
Keywords: Fitting decomposition, Engel's Theorem
Article copyright: © Copyright 1971 American Mathematical Society