Journal of Lie Theory

no. 3
C-Supplemented Subalgebras of Lie Algebras
Journal of Lie Theory, Volume 18 (2008) no. 3, pp. 717-724
A subalgebra $B$ of a Lie algebra $L$ is c-{\it supplemented} in $L$ if there is a subalgebra $C$ of $L$ with $L = B + C$ and $B \cap C \leq B_L$, where $B_L$ is the core of $B$ in $L$. This is analogous to the corresponding concept of a c-supplemented subgroup in a finite group. We say that $L$ is c-{\it supplemented} if every subalgebra of $L$ is c-supplemented in $L$. We give here a complete characterisation of c-supplemented Lie algebras over a general field.
DOI: 10.5802/jolt.520
Classification: 17B05, 17B20, 17B30, 17B50
Keywords: Lie algebras, c-supplemented subalgebras, completely factorisable algebras, Frattini ideal, subalgebras of codimension one 
@article{JOLT_2008_18_3_a13,
     author = {D. A. Towers},
     title = {C-Supplemented {Subalgebras} of {Lie} {Algebras}},
     journal = {Journal of Lie Theory},
     pages = {717--724},
     year = {2008},
     volume = {18},
     number = {3},
     doi = {10.5802/jolt.520},
     zbl = {1178.17006},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.520/}
}
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D. A. Towers. C-Supplemented Subalgebras of Lie Algebras. Journal of Lie Theory, Volume 18 (2008) no. 3, pp. 717-724. doi: 10.5802/jolt.520

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