On $n$-maximal subalgebras of Lie algebras
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Abstract:
A $2$-maximal subalgebra of a Lie algebra $L$ is a maximal subalgebra of a maximal subalgebra of $L$. Similarly we can define $3$-maximal subalgebras, and so on. There are many interesting results concerning the question of what certain intrinsic properties of the maximal subalgebras of a Lie algebra $L$ imply about the structure of $L$ itself. Here we consider whether similar results can be obtained by imposing conditions on the $n$-maximal subalgebras of $L$, where $n>1$.References
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Additional Information
- David A. Towers
- Affiliation: Department of Mathematics, Lancaster University, Lancaster LA1 4YF, United Kingdom
- MR Author ID: 173875
- Email: d.towers@lancaster.ac.uk
- Received by editor(s): February 13, 2015
- Received by editor(s) in revised form: April 20, 2015
- Published electronically: August 12, 2015
- Communicated by: Kailash C. Misra
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 1457-1466
- MSC (2010): Primary 17B05, 17B30, 17B50
- DOI: https://doi.org/10.1090/proc/12821
- MathSciNet review: 3451224