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Journal of Lie Theory 18 (2008), No. 3, 717--724
Copyright Heldermann Verlag 2008

C-Supplemented Subalgebras of Lie Algebras

David A. Towers
Dept. of Mathematics, Lancaster University, Lancaster LA1 4YF, England


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.

Keywords: Lie algebras, c-supplemented subalgebras, completely factorisable algebras, Frattini ideal, subalgebras of codimension one.

MSC: 17B05, 17B20, 17B30, 17B50

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