
Journal of Lie Theory 18 (2008), No. 3, 717724 Copyright Heldermann Verlag 2008 CSupplemented Subalgebras of Lie Algebras David A. Towers Dept. of Mathematics, Lancaster University, Lancaster LA1 4YF, England d.towers@lancaster.ac.uk [Abstractpdf] 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 csupplemented subgroup in a finite group. We say that $L$ is c{\it supplemented} if every subalgebra of $L$ is csupplemented in $L$. We give here a complete characterisation of csupplemented Lie algebras over a general field. Keywords: Lie algebras, csupplemented subalgebras, completely factorisable algebras, Frattini ideal, subalgebras of codimension one. MSC: 17B05, 17B20, 17B30, 17B50 [ Fulltextpdf (137 KB)] for subscribers only. 