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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Minimal nonnilpotent solvable Lie algebras
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by Ernest L. Stitzinger PDF
Proc. Amer. Math. Soc. 28 (1971), 47-49 Request permission

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 $A/A’$.
References
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Additional Information
  • © Copyright 1971 American Mathematical Society
  • 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