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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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Keywords: Fitting decomposition, Engel’s Theorem
Article copyright: © Copyright 1971 American Mathematical Society