Subalgebras that cover or avoid chief factors of Lie algebras
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- by David A. Towers PDF
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Abstract:
We call a subalgebra $U$ of a Lie algebra $L$ a $CAP$-subalgebra of $L$ if for any chief factor $H/K$ of $L$, we have $H \cap U = K \cap U$ or $H+U = K+U$. In this paper we investigate some properties of such subalgebras and obtain some characterizations for a finite-dimensional Lie algebra $L$ to be solvable under the assumption that some of its maximal subalgebras or $2$-maximal subalgebras be $CAP$-subalgebras.References
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Additional Information
- David A. Towers
- Affiliation: Department of Mathematics and Statistics, Lancaster University, Lancaster LA1 4YF, England
- MR Author ID: 173875
- Email: d.towers@lancaster.ac.uk
- Received by editor(s): January 31, 2014
- Received by editor(s) in revised form: April 1, 2014
- Published electronically: March 18, 2015
- Communicated by: Kailash Misra
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 3377-3385
- MSC (2010): Primary 17B05, 17B30, 17B50
- DOI: https://doi.org/10.1090/S0002-9939-2015-12533-6
- MathSciNet review: 3348780